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Simplify (sinx + cosx) ^2/ sin2x

User Chtrinh
by
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1 Answer

12 votes


\csc 2x+1

Explanation:


  • ((\sin x+\cos x)^2)/(\sin2x)

  • We expand
    (\sin x+\cos x)^2 using algebraic identity
    (a+b)^2=a^2+b^2+2ab


  • =(\sin^2x+\cos^2x+2\sin x.\cos x)/(\sin2x)


  • = (1+\sin2x)/(\sin2x)


  • =(1)/(\sin2x)+(\sin2x)/(\sin2x)


  • =\csc 2x+1
User JREN
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