Trigonometry Examples

Solve for x square root of 7sin(x)+ square root of 21cos(x)=ksin(x+x)
Step 1
Square both sides of the equation.
Step 2
Simplify .
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Step 2.1
Rewrite as .
Step 2.2
Expand using the FOIL Method.
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Step 2.2.1
Apply the distributive property.
Step 2.2.2
Apply the distributive property.
Step 2.2.3
Apply the distributive property.
Step 2.3
Simplify and combine like terms.
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Step 2.3.1
Simplify each term.
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Step 2.3.1.1
Multiply .
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Step 2.3.1.1.1
Raise to the power of .
Step 2.3.1.1.2
Raise to the power of .
Step 2.3.1.1.3
Use the power rule to combine exponents.
Step 2.3.1.1.4
Add and .
Step 2.3.1.1.5
Raise to the power of .
Step 2.3.1.1.6
Raise to the power of .
Step 2.3.1.1.7
Use the power rule to combine exponents.
Step 2.3.1.1.8
Add and .
Step 2.3.1.2
Rewrite as .
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Step 2.3.1.2.1
Use to rewrite as .
Step 2.3.1.2.2
Apply the power rule and multiply exponents, .
Step 2.3.1.2.3
Combine and .
Step 2.3.1.2.4
Cancel the common factor of .
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Step 2.3.1.2.4.1
Cancel the common factor.
Step 2.3.1.2.4.2
Rewrite the expression.
Step 2.3.1.2.5
Evaluate the exponent.
Step 2.3.1.3
Multiply .
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Step 2.3.1.3.1
Combine using the product rule for radicals.
Step 2.3.1.3.2
Multiply by .
Step 2.3.1.4
Rewrite as .
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Step 2.3.1.4.1
Factor out of .
Step 2.3.1.4.2
Rewrite as .
Step 2.3.1.5
Pull terms out from under the radical.
Step 2.3.1.6
Multiply .
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Step 2.3.1.6.1
Combine using the product rule for radicals.
Step 2.3.1.6.2
Multiply by .
Step 2.3.1.7
Rewrite as .
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Step 2.3.1.7.1
Factor out of .
Step 2.3.1.7.2
Rewrite as .
Step 2.3.1.8
Pull terms out from under the radical.
Step 2.3.1.9
Multiply .
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Step 2.3.1.9.1
Raise to the power of .
Step 2.3.1.9.2
Raise to the power of .
Step 2.3.1.9.3
Use the power rule to combine exponents.
Step 2.3.1.9.4
Add and .
Step 2.3.1.9.5
Raise to the power of .
Step 2.3.1.9.6
Raise to the power of .
Step 2.3.1.9.7
Use the power rule to combine exponents.
Step 2.3.1.9.8
Add and .
Step 2.3.1.10
Rewrite as .
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Step 2.3.1.10.1
Use to rewrite as .
Step 2.3.1.10.2
Apply the power rule and multiply exponents, .
Step 2.3.1.10.3
Combine and .
Step 2.3.1.10.4
Cancel the common factor of .
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Step 2.3.1.10.4.1
Cancel the common factor.
Step 2.3.1.10.4.2
Rewrite the expression.
Step 2.3.1.10.5
Evaluate the exponent.
Step 2.3.2
Reorder the factors of .
Step 2.3.3
Add and .
Step 3
Simplify .
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Step 3.1
Add and .
Step 3.2
Rewrite using the commutative property of multiplication.
Step 3.3
Use the power rule to distribute the exponent.
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Step 3.3.1
Apply the product rule to .
Step 3.3.2
Apply the product rule to .
Step 3.3.3
Apply the product rule to .
Step 3.4
Raise to the power of .
Step 4
Subtract from both sides of the equation.
Step 5
Replace the with based on the identity.
Step 6
Simplify each term.
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Step 6.1
Apply the distributive property.
Step 6.2
Multiply by .
Step 6.3
Multiply by .
Step 7
Add and .
Step 8
Simplify .
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Step 8.1
Simplify each term.
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Step 8.1.1
Apply the product rule to .
Step 8.1.2
Rewrite as .
Step 8.1.3
Move to the left of .
Step 8.1.4
Rewrite as .
Step 8.1.5
Multiply by .
Step 8.2
Reorder factors in .