Q) If tan θ = , then show that  =

Ans: Given that, tan θ =

   cot θ = √7

Let’s start from numerator of LHS:

cosec² θ – sec² θ = (1 + cot² θ) – (1 + tan² θ)

= cot² θ – tan² θ

= (√7)² –

= 7 –

= ………………… (i)

Similarly, let’s solve denominator of LHS:

cosec² θ + sec² θ

= (1 + cot² θ) + (1 + tan² θ)

= 2 + cot² θ + tan² θ

= 2 + (

= 9 +

= ………………….. (ii)

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

LHS =

=

= ….. RHS….  Hence Proved !