SSC CHSL 2024 PYQ — Question 68

The correct answer is option 2 i.e.  cos x ⋅ cosy - sin x ⋅ sin y - sin x ⋅ cos y + cos x ⋅ sin y + $\frac{2 \tan z}{1 - \tan^2 z}$.

​cos(x + y)=cosx.cosy - sinx.siny

sin(x - y)=sinx.cosy - cosx.siny  

tan(2z) = $\frac{2 \tan z}{1 - \tan^2 z}$

Putting it all together, we can rewrite the expression:

cos(x + y) - sin(x - y) + tan(2z)

⇒ (cosx.cosy - sinx.siny) - (sinx.cosy - cosx.siny) + tan(2z)

⇒ cosx.cosy - sinx.siny - sinx.cosy + cosx.siny + tan(2z)

⇒ cosx.cosy + cosx.siny - sinx.siny - sinx.cosy + tan(2z)