Question 31

If $$\sin \theta + \cos \theta = \dfrac{\sqrt{7}}{2}$$, then $$\sin \theta - \cos \theta$$ is equal to :

Solution

$$\sin \theta + \cos \theta = \frac{\sqrt{7}}{2}$$

Squaring both sides

$$1+2\sin\theta\cos\theta=\dfrac{7}{4}$$

$$2\sin\theta\cos\theta=\dfrac{3}{4}$$

We know that -

$$\sin\theta-\cos\theta=\sqrt{\sin^2\theta+\cos^2\theta-2\sin\theta\cos\theta}$$

$$\sin\theta-\cos\theta=\sqrt{1-\dfrac{3}{4}}$$

$$\sin\theta-\cos\theta=\dfrac{1}{2}$$

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