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# Trigonometry Examples

Rewrite as an angle where the values of the six trigonometric functions are known divided by .

Apply the tangent half-angle identity.

Change the to because tangent is positive in the first quadrant.

The exact value of is .

The exact value of is .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Multiply by .

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Multiply and .

Expand the denominator using the FOIL method.

Simplify.

Apply the distributive property.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Simplify each term.

Apply the distributive property.

Multiply .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Simplify each term.

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate the exponent.

Multiply by .

Cancel the common factor of and .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Apply the distributive property.

Multiply by .

Add and .

Subtract from .

The result can be shown in multiple forms.

Exact Form:

Decimal Form: