Question

cot square 30 degree minus 2 cos square 30 degree minus 3 by 4 sec square 45 degree + 1 by 4 cosec square 30 degree​

Answer 1

Answer:

1

Step-by-step explanation:

cot2 30 -2cos2 30 -3/4 sec2 45 +1/4 cosec2 30

=(√3)^2 - 2(√3/2)^2 -3/4(√2)^2+ 1/4 (2)^2

= 3-3/2-3/2+1

=3-3+1

=1

Answer 2

$\cot^2 30^\circ-2\cos^2 30^\circ-\frac{3}{4}\sec^2 45^\circ+\frac{1}{4}\csc ^2 30^\circ=1$

Step-by-step explanation:

Given : Expression $\cot^2 30^\circ-2\cos^2 30^\circ-\frac{3}{4}\sec^2 45^\circ+\frac{1}{4}\csc ^2 30^\circ$

To find : Simplify the expression ?

Solution :

Using trigonometric values,

$\cot 30^\circ=\sqrt{3}$

$\cos 30^\circ=\frac{\sqrt{3}}{2}$

$\sec 45^\circ=\sqrt2$

$\csc 30^\circ=2$

Substitute the value in the expression,

$=(\sqrt{3})^2-2(\frac{\sqrt{3}}{2})^2-\frac{3}{4}(\sqrt2)^2+\frac{1}{4}(2)^2$

$=3-2(\frac{3}{4})-\frac{3}{4}(2)+\frac{1}{4}(4)$

$=3-\frac{3}{2}-\frac{3}{2}+1$

$=4-\frac{6}{2}$

$=4-3$

$=1$

Therefore, $\cot^2 30^\circ-2\cos^2 30^\circ-\frac{3}{4}\sec^2 45^\circ+\frac{1}{4}\csc ^2 30^\circ=1$

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