Multiply and simplify: frac{(sin theta+cos theta)(sin theta+cos theta)-1}{sin theta cos theta}

Rui Baldwin 2021-02-21 Answered
Multiply and simplify: (sinθ+cosθ)(sinθ+cosθ)1sinθcosθ
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Expert Answer

Liyana Mansell
Answered 2021-02-22 Author has 97 answers
Use the square of a binomal:
(a+b)2=(a+b)(a+b)=a2+2ab+b2
=(sin2θ+2sincosθ+cos2θ)1sinθcosθ
=(2sinθcosθ+sin2θ+cos2θ)1sinθcosθ
Use the Pythagorean identity: sin2θ+cos2θ=1
=(2sinθcosθ+1)1sinθcosθ
Simplify:
2sinθcosθsinθcosθ=2
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