Question

Prove the following trigonometric identities.

$\mathrm{If}{\mathrm{T}}_n={\sin }^n\theta +{\cos }^n\theta ,\mathrm{prove}\mathrm{that}\frac{{\mathrm{T}}_3-{\mathrm{T}}_5}{{\mathrm{T}}_1}=\frac{{\mathrm{T}}_5-{\mathrm{T}}_7}{{\mathrm{T}}_3}$

Answer 1

In the given question, we are given

We need to prove

Here L.H.S is

Now, solving the L.H.S, we get

Further using the property, we get

So,

Now, solving the R.H.S, we get

So,

Further using the property, we get,

So,

Hence proved.