Question 56

If (1 - cosA)/2 = x, then the value of x is

Solution

Using double angle formula, we know that $$cos(2\theta) = cos^2\theta - sin^2\theta$$

=> $$cos(2\theta) = (1 - sin^2\theta) - sin^2\theta$$

=> $$cos(2\theta) = 1 - 2sin^2\theta$$

Replacing $$\theta$$ by $$\frac{A}{2}$$, we get :

=> $$cos A = 1 - 2sin^2(\frac{A}{2})$$

=> $$2sin^2(\frac{A}{2}) = 1 - cosA$$

=> $$sin^2(\frac{A}{2}) = \frac{(1-cosA)}{2}$$

=> Ans - (D)

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