Simplify and choose the correct option: (1+tanθ+secθ)(1+cotθ−cosecθ)
A
2
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B
-1
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C
0
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D
1
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Solution
The correct option is A 2 (1+tanθ+secθ)(1+cotθ−cosecθ) =(1+sinθcosθ+1cosθ)(1+cosθsinθ−1sinθ) =(cosθ+sinθ+1)cosθ×(sinθ+cosθ−1)sinθ =(cosθ+sinθ)2−12(cosθsinθ) =(cos2θ+sin2θ+2cosθsinθ−1)(cosθsinθ) =(1+2cosθsinθ−1)(cosθsinθ) =(2cosθsinθ)(cosθsinθ)=2