Trigonometry Examples

Solve for x (3pi)/4+2npi=12sin(x)cos(x)-3 square root of 2
Step 1
Rewrite the equation as .
Step 2
Add to both sides of the equation.
Step 3
Multiply each term in by to eliminate the fractions.
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Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Factor out of .
Step 3.2.1.2
Cancel the common factor.
Step 3.2.1.3
Rewrite the expression.
Step 3.2.2
Apply the sine double-angle identity.
Step 3.3
Simplify the right side.
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Step 3.3.1
Simplify each term.
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Step 3.3.1.1
Cancel the common factor of .
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Step 3.3.1.1.1
Factor out of .
Step 3.3.1.1.2
Factor out of .
Step 3.3.1.1.3
Cancel the common factor.
Step 3.3.1.1.4
Rewrite the expression.
Step 3.3.1.2
Multiply by .
Step 3.3.1.3
Multiply by .
Step 3.3.1.4
Cancel the common factor of .
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Step 3.3.1.4.1
Factor out of .
Step 3.3.1.4.2
Factor out of .
Step 3.3.1.4.3
Cancel the common factor.
Step 3.3.1.4.4
Rewrite the expression.
Step 3.3.1.5
Combine and .
Step 3.3.1.6
Combine and .
Step 3.3.1.7
Cancel the common factor of .
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Step 3.3.1.7.1
Factor out of .
Step 3.3.1.7.2
Factor out of .
Step 3.3.1.7.3
Cancel the common factor.
Step 3.3.1.7.4
Rewrite the expression.
Step 3.3.1.8
Combine and .
Step 4
Simplify .
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Step 4.1
Reorder and .
Step 4.2
Reorder and .
Step 5
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 6
Divide each term in by and simplify.
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Step 6.1
Divide each term in by .
Step 6.2
Simplify the left side.
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Step 6.2.1
Cancel the common factor of .
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Step 6.2.1.1
Cancel the common factor.
Step 6.2.1.2
Divide by .
Step 6.3
Simplify the right side.
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Step 6.3.1
Simplify the numerator.
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Step 6.3.1.1
To write as a fraction with a common denominator, multiply by .
Step 6.3.1.2
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 6.3.1.2.1
Multiply by .
Step 6.3.1.2.2
Multiply by .
Step 6.3.1.3
Combine the numerators over the common denominator.
Step 6.3.1.4
Move to the left of .