(1+\cot\theta-\csc\theta)(1+\tan\theta+\sec\theta)=

AP ICET 2017 Shift 2 Paper

Question : 120 of 200

Marks: +1, -0

(1+\cotθ-\cscθ)(1+\tanθ+\secθ)=

Solution:

(1+\cotθ-{\cosec}θ)(1+\tanθ+\secθ)

=(1+{\cosθ}/{\sinθ}-{1}/{\sinθ})(1+{\sinθ}/{\cosθ}+{1}/{\cosθ})

=\{{(\sinθ+\cosθ)-1}/{\sinθ}\}\{{(\cosθ+\sinθ)+1}/{\sinθ}\}

={(\sinθ+\cosθ)^{2}-1^{2}}/{\sinθ\cosθ}

={\sin^{2}θ+\cos^{2}θ+2\sinθ\cosθ-1}/{\sinθ\cosθ}={2\sinθ\cosθ}/{\sinθ\cosθ}=2

={1+2\sinθ\cosθ-1}/{\sinθ\cosθ}

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