Question

cot theta - 10 theta = 2 cos2 theta - 1 / sin theta cos theta

Answer 1

LHS = cot∅ - tan∅

= cos∅/sin∅ - sin∅/cos∅

= {cos²∅ - sin²∅}/sin∅.cos∅

we know,
cos²∅ + sin²∅ = 1
sin²∅ = 1 - cos²∅ put it .

= (2cos²∅ -1)/(sin∅.cos∅) = RHS

Answer 2

Hey there !!!!!

__________________________________________________

  = cotθ-tanθ

  =cosθ/sinθ-sinθ/cosθ

  =cos²θ-sin²θ/sinθcosθ

  cos²θ-sin²θ=cos2θ

  So,

  = cos2θ/sinθcosθ

But cos2θ=2cos²θ-1

So,

= 2cos²θ-1/sinθcosθ

LHS=RHS

___________________________________________________

Hope this helped you........................