Question

prove that cot^2theta-tan^2theta=cosec^2theta-sec^2theta​

Answer 1

$\large \mathfrak \pink {\leadsto~Question~:-}$

Prove the following :-

$\tt cot^2\theta -tan^2\theta = cosec^2\theta - sec^2\theta$

$\large \mathfrak \pink {\leadsto~Solution~:-}$

$\blue {:~\implies}~\tt LHS=cot^2\theta -tan^2\theta$

$\blue {:~\implies}~\tt (cosec^2\theta-1)-(sec^2\theta-1)$

$\blue {:~\implies}~\tt cosec^2\theta - 1-sec^2\theta + 1 = RHS$

$\underline {\boxed {\blue {:~\implies}~\tt LHS=RHS}}$

$\large \mathfrak \pink {\leadsto~Concepts~:-}$

$\blue {:~\implies}\tt cot^2\theta = cosec^2\theta -1$

$\blue {:~\implies}\tt tan^2\theta = sec^2\theta -1$

___________________

Hope everything's clear!

Answer 2

LHS=cot

2

θ−tan

2

θ

\blue {:~\implies}~\tt (cosec^2\theta-1)-(sec^2\theta-1): ⟹ (cosec

2

θ−1)−(sec

2

θ−1)

\blue {:~\implies}~\tt cosec^2\theta - 1-sec^2\theta + 1 = RHS: ⟹ cosec

2

θ−1−sec

2

θ+1=RHS

\underline {\boxed {\blue {:~\implies}~\tt LHS=RHS}}

: ⟹ LHS=RHS