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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

sin2ฮธ=1-cos2ฮธ2

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.

cos2ฮธ=cosฮธcosฮธ-sinฮธsinฮธ=cos2ฮธ-sin2ฮธ=1-sin2ฮธ-sin2ฮธcos2ฮธ=1-2sin2ฮธ2sin2ฮธ=1-cos2ฮธsin2ฮธ=1-cos2ฮธ2

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