Question 114

If $$\sin A - \cos A$$= $$\frac{\sqrt{3}-1}{2}$$, then the value of $$\sin A \cos A$$ is

Solution

Given, $$\sin A-\cos A=\frac{\ \sqrt{\ 3}-1}{2}$$

Squaring on both sides we get

$$\sin^2A+\cos^2A-2\sin A\cos A=\ \frac{\left(\sqrt{\ 3}\right)^2+1^2-2\sqrt{\ 3}}{4}$$

$$1-2\sin A\cos A=\ \frac{4-2\sqrt{\ 3}}{4}$$

$$2\sin A\cos A= 1-\left(\frac{4-2\sqrt{\ 3}}{4}\right)$$

$$2\sin A\cos A= \frac{4-4+2\sqrt{\ 3}}{4}$$

$$2\sin A\cos A=\frac{2\sqrt{\ 3}}{4}$$

$$\sin A\cos A=\frac{\sqrt{\ 3}}{4}$$

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