Question 127

If $$\alpha + \theta$$ = $$\frac{7\pi}{12}$$ and $$\tan \theta = \sqrt{3}$$, then the value of $$\tan \alpha$$ is:

Solution

Given : $$\tan \theta = \sqrt{3}$$

=> $$\tan \theta = tan(\frac{\pi}{3})$$

=> $$\theta=\frac{\pi}{3}$$

Also, $$\alpha + \theta$$ = $$\frac{7\pi}{12}$$

=> $$\alpha=\frac{7\pi}{12}-\frac{\pi}{3}$$

=> $$\alpha=\frac{7\pi-4\pi}{12}=\frac{\pi}{4}$$

$$\therefore$$ $$tan\alpha=tan(\frac{\pi}{4})=1$$

=> Ans - (B)

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