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# Lecture - 8 Chapter 3 Trigonometric Functions

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)