Question

If tan θ = 1/√7 show that (cosec² θ - sec² θ)/(cosec² θ + sec² θ) = 3/4

Answer 1

Let us consider a right ∆ABC, right angled at B and ∠C = θ. 

Now it is given that tan θ = AB/BC = 1/√7

So, if AB = k, then BC = √7, where k is  positive number. 

Using Pythagoras theorem, we have:

Now, finding out the values of the other trigonometric ratios, we have:

Substituting the values of cosec θ and sec θ in the give expression, we get:

i.e., LHS = RHS 

Hence proved.