Question

Prove that : cot theta -tan theta = 2 cos2 theta-1/
sin theta
cos theta​

Answer 1

To prove--->Cotθ - tanθ = (2 Cos²θ - 1 )/ Sinθ Cosθ

Proof--->

LHS = Cotθ - tanθ

We know that tanθ = Sinθ / Cosθ and

Cotθ = Cosθ / Sinθ

= ( Cosθ / Sinθ ) - ( Sinθ / Cosθ )

Taking Sinθ Cosθ as LCM

= ( Cos²θ - Sin²θ ) / Sinθ Cosθ

We have a formula,

Sin²θ = 1 - Cos²θ , applying it here , we get,

= { Cos²θ - ( 1 - Cos²θ ) } / Sinθ Cosθ

= ( Cos²θ - 1 + Cos²θ ) / Sinθ Cosθ

= ( 2 Cos²θ - 1 ) / Sinθ Cosθ = RHS

Additional information--->

1) 1 + tan²θ = Sec²θ

2) 1 + Cot²θ = Cosec²θ

3) Secθ = 1 / Cosθ

4) Cosecθ = 1 / Sinθ

Answer 2

Step-by-step explanation:

two photu given above and plese follow and like please