If $$tan3\theta\times tan7\theta=1$$, then the value of $$tan(\theta+36^{\circ})$$ is
Given : $$tan3\theta\times tan7\theta=1$$
=> $$tan3\theta=\frac{1}{tan7\theta}$$
=> $$tan3\theta=cot7\theta$$
=> $$tan3\theta=tan(90^\circ-7\theta)$$
=> $$3\theta=90^\circ-7\theta$$
=> $$3\theta+7\theta=10\theta=90^\circ$$
=> $$\theta=\frac{90}{10}=9^\circ$$
$$\therefore$$Â $$tan(\theta+36^{\circ})$$
= $$tan(9+36)^\circ=tan(45^\circ)=1$$
=> Ans - (C)Â
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