Question 69

If $$\pi sin\theta=1,\pi cos\theta=1$$ then $$\sqrt{3}tan(\frac{2}{3}\theta)+1$$ the value is

Solution

Given : $$\pi sin\theta=1,\pi cos\theta=1$$

=> $$sin\theta=cos\theta$$

=> $$sin\theta=sin(90^\circ-\theta)$$

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

=> $$\theta+\theta=2\theta=90^\circ$$

=> $$\theta=\frac{90}{2}=45^\circ$$

To find : $$\sqrt{3}tan(\frac{2}{3}\theta)+1$$

= $$\sqrt{3}tan(\frac{2}{3} \times 45^\circ)+1$$

= $$\sqrt{3}tan(30^\circ)+1$$

= $$(\sqrt3 \times \frac{1}{\sqrt{3}})+1$$

= $$1+1=2$$

=> Ans - (C)

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