The pain you feel today will be the strength you feel tomorrow.

Derivation for thrice angles
\( \sin 3x = 3 \sin x – 4 \sin^3 x\)
\( \cos 3x = 4 \cos^3 x – 3 \cos x\)
\( \tan 3x = \frac{3 \tan x – \tan^3 x}{1-3\tan^2 x}\)

Derivation for
\( \sin A + \sin B = 2 \sin \left ( \frac{A+B}{2} \right ) \cos \left ( \frac{A-B}{2} \right )\)
\( \sin A – \sin B = 2 \cos \left ( \frac{A+B}{2} \right ) \sin \left ( \frac{A-B}{2} \right )\)

\( \cos A + \cos B = 2 \cos \left ( \frac{A+B}{2} \right ) \cos \left ( \frac{A-B}{2} \right )\)

\( \cos A – \cos B = – 2 \sin \left ( \frac{A+B}{2} \right ) \sin \left ( \frac{A-B}{2} \right )\)

Question 12 \( \sin^2 6x – \sin^2 4x = \sin 2x \sin 10x\)

Question 13 \( \cos^2 2x – \cos^2 6x = \sin 4x \sin 8x \)

Question 14 \( \sin2 x + 2 \sin 4x + \sin 6x = 4 \cos^2 x \sin 4x\)

Question 15 \( \cot 4x (\sin 5x + \sin 3x) = \cot x (\sin 5x – \sin 3x)\)