Question 122

The value of X in the equation $$tan^2 \frac{\pi}{4}-Cos^2 \frac{\pi}{3}-X\ Sin\frac{\pi}{4}Cos\frac{\pi}{4}Tan\frac{\pi}{3}$$ is:

Solution

Expression : $$tan^2 \frac{\pi}{4}-Cos^2 \frac{\pi}{3}-X\ Sin\frac{\pi}{4}Cos\frac{\pi}{4}Tan\frac{\pi}{3}=0$$

=> $$(1)^2-(\frac{1}{4})^2-x(\frac{1}{\sqrt2})(\frac{1}{\sqrt2})(\sqrt3)=0$$

=> $$1-\frac{1}{4}-\frac{x\sqrt3}{2}=0$$

=> $$\frac{3}{4}=\frac{x\sqrt3}{2}$$

=> $$x=\frac{3}{4}\times\frac{2}{\sqrt3}$$

=> $$x=\frac{\sqrt3}{2}$$

=> Ans - (A)

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