Trigonometry Examples

Simplify ( square root of 14(cos(85)+isin(85)))^6
Step 1
Apply the distributive property.
Step 2
Use the Binomial Theorem.
Step 3
Simplify terms.
Tap for more steps...
Step 3.1
Simplify each term.
Tap for more steps...
Step 3.1.1
Apply the product rule to .
Step 3.1.2
Rewrite as .
Tap for more steps...
Step 3.1.2.1
Use to rewrite as .
Step 3.1.2.2
Apply the power rule and multiply exponents, .
Step 3.1.2.3
Combine and .
Step 3.1.2.4
Cancel the common factor of and .
Tap for more steps...
Step 3.1.2.4.1
Factor out of .
Step 3.1.2.4.2
Cancel the common factors.
Tap for more steps...
Step 3.1.2.4.2.1
Factor out of .
Step 3.1.2.4.2.2
Cancel the common factor.
Step 3.1.2.4.2.3
Rewrite the expression.
Step 3.1.2.4.2.4
Divide by .
Step 3.1.3
Raise to the power of .
Step 3.1.4
Apply the product rule to .
Step 3.1.5
Multiply by by adding the exponents.
Tap for more steps...
Step 3.1.5.1
Move .
Step 3.1.5.2
Multiply by .
Tap for more steps...
Step 3.1.5.2.1
Raise to the power of .
Step 3.1.5.2.2
Use the power rule to combine exponents.
Step 3.1.5.3
Add and .
Step 3.1.6
Rewrite as .
Tap for more steps...
Step 3.1.6.1
Use to rewrite as .
Step 3.1.6.2
Apply the power rule and multiply exponents, .
Step 3.1.6.3
Combine and .
Step 3.1.6.4
Cancel the common factor of and .
Tap for more steps...
Step 3.1.6.4.1
Factor out of .
Step 3.1.6.4.2
Cancel the common factors.
Tap for more steps...
Step 3.1.6.4.2.1
Factor out of .
Step 3.1.6.4.2.2
Cancel the common factor.
Step 3.1.6.4.2.3
Rewrite the expression.
Step 3.1.6.4.2.4
Divide by .
Step 3.1.7
Raise to the power of .
Step 3.1.8
Multiply by .
Step 3.1.9
Apply the product rule to .
Step 3.1.10
Rewrite as .
Tap for more steps...
Step 3.1.10.1
Use to rewrite as .
Step 3.1.10.2
Apply the power rule and multiply exponents, .
Step 3.1.10.3
Combine and .
Step 3.1.10.4
Cancel the common factor of and .
Tap for more steps...
Step 3.1.10.4.1
Factor out of .
Step 3.1.10.4.2
Cancel the common factors.
Tap for more steps...
Step 3.1.10.4.2.1
Factor out of .
Step 3.1.10.4.2.2
Cancel the common factor.
Step 3.1.10.4.2.3
Rewrite the expression.
Step 3.1.10.4.2.4
Divide by .
Step 3.1.11
Raise to the power of .
Step 3.1.12
Multiply by .
Step 3.1.13
Use the power rule to distribute the exponent.
Tap for more steps...
Step 3.1.13.1
Apply the product rule to .
Step 3.1.13.2
Apply the product rule to .
Step 3.1.14
Rewrite as .
Tap for more steps...
Step 3.1.14.1
Use to rewrite as .
Step 3.1.14.2
Apply the power rule and multiply exponents, .
Step 3.1.14.3
Combine and .
Step 3.1.14.4
Cancel the common factor of .
Tap for more steps...
Step 3.1.14.4.1
Cancel the common factor.
Step 3.1.14.4.2
Rewrite the expression.
Step 3.1.14.5
Evaluate the exponent.
Step 3.1.15
Rewrite as .
Step 3.1.16
Multiply by .
Step 3.1.17
Multiply by .
Step 3.1.18
Apply the product rule to .
Step 3.1.19
Rewrite as .
Step 3.1.20
Raise to the power of .
Step 3.1.21
Rewrite as .
Tap for more steps...
Step 3.1.21.1
Factor out of .
Step 3.1.21.2
Rewrite as .
Step 3.1.22
Pull terms out from under the radical.
Step 3.1.23
Multiply by .
Step 3.1.24
Use the power rule to distribute the exponent.
Tap for more steps...
Step 3.1.24.1
Apply the product rule to .
Step 3.1.24.2
Apply the product rule to .
Step 3.1.25
Multiply by by adding the exponents.
Tap for more steps...
Step 3.1.25.1
Move .
Step 3.1.25.2
Multiply by .
Tap for more steps...
Step 3.1.25.2.1
Raise to the power of .
Step 3.1.25.2.2
Use the power rule to combine exponents.
Step 3.1.25.3
Add and .
Step 3.1.26
Rewrite as .
Tap for more steps...
Step 3.1.26.1
Use to rewrite as .
Step 3.1.26.2
Apply the power rule and multiply exponents, .
Step 3.1.26.3
Combine and .
Step 3.1.26.4
Cancel the common factor of and .
Tap for more steps...
Step 3.1.26.4.1
Factor out of .
Step 3.1.26.4.2
Cancel the common factors.
Tap for more steps...
Step 3.1.26.4.2.1
Factor out of .
Step 3.1.26.4.2.2
Cancel the common factor.
Step 3.1.26.4.2.3
Rewrite the expression.
Step 3.1.26.4.2.4
Divide by .
Step 3.1.27
Raise to the power of .
Step 3.1.28
Multiply by .
Step 3.1.29
Factor out .
Step 3.1.30
Rewrite as .
Step 3.1.31
Rewrite as .
Step 3.1.32
Multiply by .
Step 3.1.33
Apply the product rule to .
Step 3.1.34
Rewrite as .
Tap for more steps...
Step 3.1.34.1
Use to rewrite as .
Step 3.1.34.2
Apply the power rule and multiply exponents, .
Step 3.1.34.3
Combine and .
Step 3.1.34.4
Cancel the common factor of .
Tap for more steps...
Step 3.1.34.4.1
Cancel the common factor.
Step 3.1.34.4.2
Rewrite the expression.
Step 3.1.34.5
Evaluate the exponent.
Step 3.1.35
Multiply by .
Step 3.1.36
Use the power rule to distribute the exponent.
Tap for more steps...
Step 3.1.36.1
Apply the product rule to .
Step 3.1.36.2
Apply the product rule to .
Step 3.1.37
Rewrite as .
Tap for more steps...
Step 3.1.37.1
Use to rewrite as .
Step 3.1.37.2
Apply the power rule and multiply exponents, .
Step 3.1.37.3
Combine and .
Step 3.1.37.4
Cancel the common factor of and .
Tap for more steps...
Step 3.1.37.4.1
Factor out of .
Step 3.1.37.4.2
Cancel the common factors.
Tap for more steps...
Step 3.1.37.4.2.1
Factor out of .
Step 3.1.37.4.2.2
Cancel the common factor.
Step 3.1.37.4.2.3
Rewrite the expression.
Step 3.1.37.4.2.4
Divide by .
Step 3.1.38
Raise to the power of .
Step 3.1.39
Rewrite as .
Tap for more steps...
Step 3.1.39.1
Rewrite as .
Step 3.1.39.2
Rewrite as .
Step 3.1.39.3
Raise to the power of .
Step 3.1.40
Multiply by .
Step 3.1.41
Multiply by .
Step 3.1.42
Use the power rule to distribute the exponent.
Tap for more steps...
Step 3.1.42.1
Apply the product rule to .
Step 3.1.42.2
Apply the product rule to .
Step 3.1.43
Multiply by by adding the exponents.
Tap for more steps...
Step 3.1.43.1
Move .
Step 3.1.43.2
Multiply by .
Tap for more steps...
Step 3.1.43.2.1
Raise to the power of .
Step 3.1.43.2.2
Use the power rule to combine exponents.
Step 3.1.43.3
Add and .
Step 3.1.44
Rewrite as .
Tap for more steps...
Step 3.1.44.1
Use to rewrite as .
Step 3.1.44.2
Apply the power rule and multiply exponents, .
Step 3.1.44.3
Combine and .
Step 3.1.44.4
Cancel the common factor of and .
Tap for more steps...
Step 3.1.44.4.1
Factor out of .
Step 3.1.44.4.2
Cancel the common factors.
Tap for more steps...
Step 3.1.44.4.2.1
Factor out of .
Step 3.1.44.4.2.2
Cancel the common factor.
Step 3.1.44.4.2.3
Rewrite the expression.
Step 3.1.44.4.2.4
Divide by .
Step 3.1.45
Raise to the power of .
Step 3.1.46
Multiply by .
Step 3.1.47
Factor out .
Step 3.1.48
Rewrite as .
Tap for more steps...
Step 3.1.48.1
Rewrite as .
Step 3.1.48.2
Rewrite as .
Step 3.1.48.3
Raise to the power of .
Step 3.1.49
Multiply by .
Step 3.1.50
Use the power rule to distribute the exponent.
Tap for more steps...
Step 3.1.50.1
Apply the product rule to .
Step 3.1.50.2
Apply the product rule to .
Step 3.1.51
Rewrite as .
Tap for more steps...
Step 3.1.51.1
Use to rewrite as .
Step 3.1.51.2
Apply the power rule and multiply exponents, .
Step 3.1.51.3
Combine and .
Step 3.1.51.4
Cancel the common factor of and .
Tap for more steps...
Step 3.1.51.4.1
Factor out of .
Step 3.1.51.4.2
Cancel the common factors.
Tap for more steps...
Step 3.1.51.4.2.1
Factor out of .
Step 3.1.51.4.2.2
Cancel the common factor.
Step 3.1.51.4.2.3
Rewrite the expression.
Step 3.1.51.4.2.4
Divide by .
Step 3.1.52
Raise to the power of .
Step 3.1.53
Factor out .
Step 3.1.54
Rewrite as .
Tap for more steps...
Step 3.1.54.1
Rewrite as .
Step 3.1.54.2
Rewrite as .
Step 3.1.54.3
Raise to the power of .
Step 3.1.55
Multiply by .
Step 3.1.56
Rewrite as .
Step 3.1.57
Multiply by .
Step 3.2
Simplify the expression.
Tap for more steps...
Step 3.2.1
Reorder factors in .
Step 3.2.2
Reorder and .
Step 3.2.3
Reorder and .
Step 3.2.4
Reorder and .