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Question:

Choose the correct option. Justify your choice (1+tanθ+secθ)(1+cotθ−cosec θ)

-1;

1

0

2

Solution:

The correct option is D 2
The value of (1+tanθ+secθ)(1+cotθ−cosec θ) = (1+sinθ/cosθ+1/cosθ)(1+cosθ/sinθ−1/sinθ) = (cosθ+sinθ+1)/cosθ * (sinθ+cosθ−1)/sinθ = (sinθ+cosθ)²−1²/sinθcosθ = sin²θ+cos²θ+2sinθcosθ−1/sinθcosθ = 2sinθcosθ/sinθcosθ = 2