List of top Mathematics Questions on Trigonometric Functions of Sum and Difference of Two Angles

If $ A, B $ and $ C $ are interior angles of a triangle $ ABC $, then $ \tan\left(\frac{A+B}{2}\right) = \dots $

In the figure, the value of cosec A is

Prove that.  \(2sin^2 \frac{π}{6}+cosec^2 \frac{7π}{6}–cos^2 \frac{π}{3}=\frac{3}{2}\)

Prove that  \(cot^2 \frac{π}{6}+cosec \frac{5π}{6}+3\,tan^2 \frac{π}{6}=6\)

Prove that  \(2sin^2 \frac{3π}{4}+2\,cos^2 \frac{π}{4}+2\,sec^2 \frac{π}{3}=10\)

Find the value of (i) sin 75° (ii) tan 15°

Prove that, \(cos(\frac{\pi}{4}-x)cos(\frac{\pi}{4}-y)-sin(\frac{\pi}{4}-x)sin(\frac{\pi}{4}-y)=sin(x+y)\)

Prove that, \(\frac{tan(\frac{π}{4}-x)}{tan(\frac{π}{4}-x)}=(\frac{1+tan x}{1-tan x})^2.\)

Prove that. \(\frac{cos(π+x)cos(-x)}{sin(π-x)cos(\frac{π}{2}+x)}=cot^2x\)

Prove that. sin(n+1) xsin(n+2)x+cos(n+1) xcos(n+2)x=cosx.

Prove that  \(cos(\frac{3{\pi}}{4}+x)-cos(\frac{3{\pi}}{4}-x)=√2sin\,x\)

Prove that sin² 6x-sin² 4x=sin 2x sin 10x

Prove that cos² 2x-cos² 6x = sin 4x sin 8x

Prove that cot 4x (sin 5x+sin 3x)=cot x (sin 5x-sin 3x)

Prove that \(\frac{cos 9x-cos5x}{sin\,17x-sin3x}=-\frac{sin\,2x}{cos\,10x}\)

Prove that \(\frac{sin5x+sin3x}{sin\,7x+cos3x}=tan\,4x\)

Prove that  \(\frac{sinx-siny}{cosx+cos y}=tan \frac{x-y}{2}.\)

Prove that  \(\frac{sinx-sin3x}{cosx+cos 3x}=tan 2x.\)

Prove that  \(\frac{sinx-sin3x}{sin^2x+cos^2x}=2\,sin\,x\).

Prove that  \(\frac{cos4x+cos3x+cos2x}{sin4x+sin3x+sin2x}=cot\,3x\).

Prove that cotx cot2x-cot2x cot3x-cot3x cotx=1.

Prove that \(tan\,4x=\frac{4\,tanx(1-tan^2x)}{1-6\,tan^2x+tan^4x}\).

Prove that cos 4x =1-8 sin² x cos² x