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Double-angle identities: Use double-angle identities to rewrite each of the following trigonometric expressions until no exponents are involved.

sin2x=_____

Short Answer

Expert verified

sin2θ=1-cos2θ2

Step by step solution

01

Step 1. Given information.

Consider the given expression,

sin2x

02

Step 2. Explanation.

Write the given trigonometric expression in cosine form.

cos2θ=cosθcosθ-sinθsinθ=cos2θ-sin2θ=1-sin2θ-sin2θcos2θ=1-2sin2θ2sin2θ=1-cos2θsin2θ=1-cos2θ2

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Most popular questions from this chapter

Solve each of the integrals in Exercises 39–74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

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