Question

Prove that (cosec theta-sin theta)(sec theta-cos theta)(tan theta-cot theta)=1

Answer 1

Answer:-

LHS:-

=>(1/sin θ-sin θ)(1/cos θ-cos θ)(tan θ+1/ tan θ)

=>1- sin ² θ/ sin θ(1- cos ²θ)/ cos θ (1+ tan ² θ)/tanθ

=>cos θ sin θ (1/ cos ² θ)/( sin θ / cos θ)

=>cos θ sin θ(1/sin θ cosθ)

=>cos θ sin θ/ sin θ cos θ

=> 1= RHS...

Answer 2

Answer:

$cosec \alpha \sec( \gamma = 1)$