How simplify (\sin X-\cos X)^{2}?

Aneeka Hunt

Aneeka Hunt

Answered question

2021-10-02

How simplify (sinXcosX)2?

Answer & Explanation

Leonard Stokes

Leonard Stokes

Skilled2021-10-03Added 98 answers

Given:
(sinxcosx)2
Let us use (ab)2=a22ab+b2
(sinxcosx)2=(sinx)22sinxcosx+(cosx)2
=sin2x2sinxcosx+cos2x
=(sin2x+cos2x)2sinxcosx
=12sinxcosx   sin2x+cos2x=1
=1sin(2x)   sin(2x)=2sinxcosx
Answer 1sin(2x)

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