Question 51

If $$\sec \theta (\cos \theta + \sin \theta) = \surd2$$, then what is the value of $$\frac{(2 \sin \theta)}{(\cos \theta - \sin \theta)}$$?

Solution

$$\sec\theta(\cos\theta+\sin\theta)=\surd2$$

or, $$(1+\tan\theta)=\surd2\ .$$

or,$$\theta=\tan^{-1}\left(\sqrt{2}-1\right)=22.5^{\circ\ }\ .$$

So,

$$\frac{(2\sin\theta)}{(\cos\theta-\sin\theta)}\ $$

$$=\frac{(2\sin22.5^{\circ\ })}{(\cos22.5^{\circ\ }-\sin22.5^{\circ\ })}\ $$

$$=1.41=\sqrt{2}\ .$$

D is correct choice.

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