Question

prove:cos²∅-tan²∅=cosec²∅-sec²∅.​

Answer 1

Step-by-step explanation:

LHS = cot²θ - tan²θ

We know from Trigonometric identities ,

cosec²α - cot²α = 1 ⇒cot²α = cosec²α - 1

sec²α - tan²α = 1 ⇒tan²α = sec²α - 1

Hence, LHS = (cosec²θ - 1) - (sec²θ - 1)

= cosec²θ - 1 - sec²θ + 1

= cosec²θ - sec²θ = $\bf{RHS}$

LHS = RHS

Hence, proved:

Answer 2

Step-by-step explanation:

LHS = cot²θ - tan²θ

We know from Trigonometric identities ,

cosec²α - cot²α = 1 ⇒cot²α = cosec²α - 1

sec²α - tan²α = 1 ⇒tan²α = sec²α - 1

Hence, LHS = (cosec²θ - 1) - (sec²θ - 1)

= cosec²θ - 1 - sec²θ + 1

= cosec²θ - sec²θ = RHS

LHS = RHS

Hence, proved: