Trigonometry Examples

Solve for x 1/2*(cot(x)+tan(x))=csc(2x)
Step 1
Simplify the left side.
Tap for more steps...
Step 1.1
Simplify .
Tap for more steps...
Step 1.1.1
Simplify each term.
Tap for more steps...
Step 1.1.1.1
Rewrite in terms of sines and cosines.
Step 1.1.1.2
Rewrite in terms of sines and cosines.
Step 1.1.2
Simplify terms.
Tap for more steps...
Step 1.1.2.1
Apply the distributive property.
Step 1.1.2.2
Multiply by .
Step 1.1.2.3
Multiply by .
Step 2
Simplify the right side.
Tap for more steps...
Step 2.1
Rewrite in terms of sines and cosines.
Step 3
Multiply both sides of the equation by .
Step 4
Apply the distributive property.
Step 5
Combine and .
Step 6
Combine and .
Step 7
Simplify each term.
Tap for more steps...
Step 7.1
Simplify the numerator.
Tap for more steps...
Step 7.1.1
Apply the sine double-angle identity.
Step 7.1.2
Combine exponents.
Tap for more steps...
Step 7.1.2.1
Raise to the power of .
Step 7.1.2.2
Raise to the power of .
Step 7.1.2.3
Use the power rule to combine exponents.
Step 7.1.2.4
Add and .
Step 7.2
Cancel the common factor of .
Tap for more steps...
Step 7.2.1
Cancel the common factor.
Step 7.2.2
Rewrite the expression.
Step 7.3
Cancel the common factor of .
Tap for more steps...
Step 7.3.1
Cancel the common factor.
Step 7.3.2
Divide by .
Step 7.4
Simplify the numerator.
Tap for more steps...
Step 7.4.1
Apply the sine double-angle identity.
Step 7.4.2
Combine exponents.
Tap for more steps...
Step 7.4.2.1
Raise to the power of .
Step 7.4.2.2
Raise to the power of .
Step 7.4.2.3
Use the power rule to combine exponents.
Step 7.4.2.4
Add and .
Step 7.5
Cancel the common factor of .
Tap for more steps...
Step 7.5.1
Cancel the common factor.
Step 7.5.2
Rewrite the expression.
Step 7.6
Cancel the common factor of .
Tap for more steps...
Step 7.6.1
Cancel the common factor.
Step 7.6.2
Divide by .
Step 8
Rearrange terms.
Step 9
Apply pythagorean identity.
Step 10
Cancel the common factor of .
Tap for more steps...
Step 10.1
Cancel the common factor.
Step 10.2
Rewrite the expression.
Step 11
Since , the equation will always be true for any value of .
All real numbers
Step 12
The result can be shown in multiple forms.
All real numbers
Interval Notation: