Question 44

If θ is positive acute angle and $$4sin^{2}$$θ = 3, then the value of tan θ - cot θ/2 is

Solution

Given : $$4sin^{2}$$θ = 3

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

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

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

=> $$\theta = 60^\circ$$

To find : tan θ - cot θ/2

= $$tan(60^\circ)-cot(30^\circ)$$

= $$\sqrt{3}-\sqrt{3}=0$$

=> Ans - (B)

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