Question 69

If $$tan3\theta\times tan7\theta=1$$, then the value of $$tan(\theta+36^{\circ})$$ is

Solution

Given : $$tan3\theta\times tan7\theta=1$$

=> $$tan3\theta=\frac{1}{tan7\theta}$$

=> $$tan3\theta=cot7\theta$$

=> $$tan3\theta=tan(90^\circ-7\theta)$$

=> $$3\theta=90^\circ-7\theta$$

=> $$3\theta+7\theta=10\theta=90^\circ$$

=> $$\theta=\frac{90}{10}=9^\circ$$

$$\therefore$$ $$tan(\theta+36^{\circ})$$

= $$tan(9+36)^\circ=tan(45^\circ)=1$$

=> Ans - (C)

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