Choose the correct answer

The value of is

We need to find the value of

Let,

Let us find sin a and cos b.

For sin a,

We know the trigonometric identity, sin² a + cos² a = 1

⇒ sin² a = 1 – cos² a

⇒ sin a = √(1 – cos² a)

Substituting the value of cos a,

We have .

So, we can find tan a.

⇒ tan a = 7 …(i)

For cos b,

We know the trigonometric identity,

sin² b + cos² b = 1

⇒ cos² b = 1 – sin² b

⇒ cos b = √(1 – sin² b)

Substituting the value of sin b,

We have .

So, we can find tan b.

⇒ tan b = 4 …(ii)

We can write as,

Now, we need to solve Right Hand Side (RHS).

We know the trigonometric identity,

Substituting the values of tan a and tan b from (i) and (ii),

So,