Question 132

If x ($$\sin$$ 60) $$\tan^{2}$$ 30° - $$\tan$$ 45° = cosec 60° $$\cot$$ 30° - $$\sec^{2}$$ 45°, then x =

Solution

sin 60 = $$\frac{\surd3}{2}$$

tan 30 = $$\frac{1}{\surd3}$$

tan 45 = 1

cosec 60 = $$\frac{2}{\surd3}$$

cot 30 = $$\surd3$$

sec 45 = $$\surd2$$

using the above values in: x sin 60° $$tan^{2}$$ 30° - tan 45° = cosec 60° cot 30° - $$sec^{2}$$ 45°

x $$\times \frac{\surd3}{2} \times$$ $$\frac{1}{\surd3}^2$$ - 1 = $$\frac{2}{\surd3} \times$$ $$\surd3$$ - $$\surd2 ^2$$

x = 2$$\surd3$$

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