**Q) **If tan θ = , then show that =

**Ans: **Given that, tan θ =

cot θ = √7

Let’s start from numerator of LHS:

cosec^{2} θ – sec^{2} θ = (1 + cot^{2} θ) – (1 + tan^{2} θ)

= cot^{2} θ – tan^{2} θ

= (√7)^{2} –

= 7 –

= ………………… (i)

Similarly, let’s solve denominator of LHS:

cosec^{2} θ + sec^{2} θ

= (1 + cot^{2} θ) + (1 + tan^{2} θ)

= 2 + cot^{2} θ + tan^{2} θ

= 2 + (

= 9 +

= ………………….. (ii)

Now, let’s put the values from equation (i) and equation (ii) in LHS, we get:

LHS =

=

= ….. RHS…. **Hence Proved !**