Question 121

If $$4Sin^2\theta-1=0$$ and angle$$\theta$$ is less than $$90^\circ$$. Then the value of $$Cos^2\theta + tan^2\theta$$ is:
Take $$(0^0<\theta<90^0)$$

Solution

Given : $$4sin^2\theta-1=0$$

=> $$4sin^2\theta=1$$

=> $$sin^2\theta=\frac{1}{4}$$

=> $$sin\theta=\sqrt{\frac{1}{4}}=\frac{1}{2}$$

=> $$\theta=sin^{-1}(\frac{1}{2})$$

=> $$\theta=30^\circ$$

To find : $$Cos^2\theta + tan^2\theta$$

= $$cos^2(30^\circ)+tan^2(30^\circ)$$

= $$(\frac{\sqrt3}{2})^2+(\frac{1}{\sqrt3})^2$$

= $$\frac{3}{4}+\frac{1}{3}=\frac{13}{12}$$

=> Ans - (B)

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