Evaluate the following: ^230^ -2 ^230^ - 34 ^245^ + 14cosec^230^ - Vidyadip

Question

Evaluate the following:
$\cot^230^\circ-2\cos^230^\circ-\frac34\sec^245^\circ+\frac14\text{cosec}^230^\circ$

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Answer

On substituting values of various T-ratious, we get:
$\cot^230^\circ-2\cos^230^\circ-\frac34\sec^245^\circ+\frac14\text{cosec}^230^\circ$
$=\big(\sqrt{3}\big)^2-2\times\Big(\frac{\sqrt{3}}{2}\Big)^2-\frac34\times\big(\sqrt{2}\big)^2+\frac14\times(2)^2$
$=3-2\times\frac34-\frac34\times2+\frac14\times4$
$=3-\frac32-\frac32+1$
$=4-\Big(\frac{3}{2}+\frac{3}{2}\Big)$
$=4-3$
$=1$

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