Solve the equationfrac{cot(x)-tan(x)}{(cot^{2}(x)-tan^{2}(x)}=sin xcos x

nicekikah 2021-02-19 Answered

Solve the equation cot(x)tan(x)(cot2(x)tan2(x)=sinxcosx

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Expert Answer

Ezra Herbert
Answered 2021-02-20 Author has 99 answers

Apply Difference of Two Squares Formula:
x2y2=(x+y)(xy)
cot2(x)tan2(x)=(cot(x)+tan(x))(cot(x)tan(x))
cot(x)tan(x)cot2(x)tan2(x)=cot(x)tan(x)(cot(x)+tan(x))(cot(x)tan(x))=1(cot(x)+tan(x)
=12csc(2x)
=sin(2x)2
=sinxcosx
Therefore
a2a2sin2(θ)=acos(θ)

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