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If cos x=- (1)/(3) and x lies in Qu...

If cos ` x=- (1)/(3) ` and x lies in Quadrant III find the values of
`(i) " sin " (x)/(2) , (ii) " cos " (x)/(2) , (iii) " tan " (x)/(2)`

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AI Generated Solution

To solve the problem step by step, we need to find the values of \( \sin \frac{x}{2} \), \( \cos \frac{x}{2} \), and \( \tan \frac{x}{2} \) given that \( \cos x = -\frac{1}{3} \) and \( x \) lies in Quadrant III. ### Step 1: Find \( \sin x \) Using the Pythagorean identity: \[ \sin^2 x + \cos^2 x = 1 \] Substituting the value of \( \cos x \): ...
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