Question 141
If 2cos$$^{2}$$ θ - 1 = 0 and θ is acute, then what is the value of (cot$$^{2}$$ θ - tan$$^{2}$$ θ)?
Solution
Given : $$2cos^2\theta-1=0$$
=> $$cos^2\theta=\frac{1}{2}$$
=> $$cos\theta=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt2}$$
=> $$\theta=cos^{-1}(\frac{1}{\sqrt2})=45^\circ$$
$$\therefore$$ $$cot^2\theta-tan^2\theta$$
= $$cot^2(45^\circ)-tan^2(45^\circ)$$
= $$1-1=0$$
=> Ans - (A)
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