Question 132

If θ is positive acute angle and $$3 (sec^2 θ + tan^2 θ) = 5$$, then which one is true ?

Solution

Given : $$3 (sec^2 θ + tan^2 θ) = 5$$

=> $$sec^2 θ + tan^2 θ = \frac{5}{3}$$ ------------(i)

Also, $$sec^2\theta-tan^2\theta=1$$ -------------(ii)

Adding both equations, => $$2sec^2\theta=\frac{8}{3}$$

=> $$cos^2\theta=\frac{3}{4}$$

=> $$cos\theta=\frac{\sqrt3}{2}=cos(30^\circ)$$

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

Now, $$cos(60^\circ)=sin(30^\circ)$$

=> $$cos(2\theta)=sin(\theta)$$

=> Ans - (B)

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