Question 141

If 4sin$$^{2}$$ 2θ - 3 = 0 and θ is acute, then what is the value of (cot$$\ ^{2}\ $$ θ + tan $$^{2}$$ θ)?

Solution

Given : $$4sin^22\theta-3=0$$

=> $$sin^22\theta=\frac{3}{4}$$

=> $$sin2\theta=\sqrt{\frac{3}{4}}=\frac{\sqrt3}{2}$$

=> $$sin2\theta=sin(60^\circ)$$

=> $$2\theta=60$$

=> $$\theta=\frac{60}{2}=30^\circ$$

$$\therefore$$ $$cot^2\theta+tan^2\theta$$

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

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

= $$3+\frac{1}{3}=\frac{10}{3}$$

=> Ans - (C)

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