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# Lecture - 11 Chapter 3 Trigonometric Functions

Derivation for half angles, sin(x/2), cos(x/2) and tan(x/2)

Example 27 Find the value of \( \tan \frac{\pi}{8}\)

Example 28 If \( \tan x = \frac {3}{4}, \pi < x < \frac{3\pi}{2}\), find the value of sin(x/2), cos(x/2) and tan(x/2).

Find sin(x/2), cos(x/2) and tan(x/2) in each of the following:

Question 8 \( \tan x = \frac{-4}{3}\), *x * in the quadrant II.

Question 9 \( \cos x = \frac{-1}{3}\), *x * in the quadrant III.

Question 10 \( \sin x = \frac{1}{4}\), *x * in the quadrant II.

Example 29 Prove that \( \cos^2 x + \cos^2 \left ( x + \frac{\pi}{3} \right ) + \cos^2 \left ( x – \frac{\pi}{3} \right ) = \frac{3}{2}\)

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