Question

find the value of cosec⁴-cosec²​

Answer 1

Step-by-step explanation:

cosec⁴-cosec²

= cosec²(cosec²-1) ;[ taking cosec² common]

= 1+cot²(cot²) ;[putting values of both]

= cot² + cot⁴ , proved .

Answer 2

Step-by-step explanation:

As we know that,

cosec²θ = 1 + cot²θ ...(i)

Given : LHS = cosec⁴θ - cosec²θ

Taking cosec²θ as common.

→ cosec²θ (cosec²θ - 1)

→ 1 + cot²θ (1 + cot²θ - 1) ...[ using (i) ]

→ 1 + cot²θ (cot²θ + 1 - 1)

→ 1 + cot²θ (cot²θ)

→ cot²θ + cot⁴θ

RHS

Hence, proved !!