Question

If sec θ = 17/8 verify that (3 - 4sin² θ)/(4cos² θ - 3) = (3 - tan² θ)/(1 - tan³ θ)

Answer 1

It is given that sec θ = 17/8 

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

We know that cos θ = 1/sec θ = 8/17 = BC/AC

So, if BC = 8k, then AC = 17k, where k is a positive number. 

Using Pythagoras theorem, we have:

Now, tan θ = AB/BC = 15/8 and sin θ = AB/AC = 15k/17k = 15/17

The given expression is

Substituting the values in the above expression, we get:

∴ LHS = RHS 

Hence proved.