Question

Evaluate : 4 cot2 45° – sec2 60° + sin2 60° + cos2 90°.

Answer 1

Answer:

4 cot2 45° - sec 2 60° + sin 2 60° + cos 2 90 °

4*1 - 4 + 3/4 + 0

3/4

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Answer 2

$4\cot^2 45^\circ-\sec^2 60^\circ+\sin^2 60^\circ+\cos^2 90^\circ=\frac{1}{2}$

Step-by-step explanation:

Given : Expression $4\cot^2 45^\circ-\sec^2 60^\circ+\sin^2 60^\circ+\cos^2 90^\circ$

To find : Evaluate the expression ?

Solution :

Expression $4\cot^2 45^\circ-\sec^2 60^\circ+\sin^2 60^\circ+\cos^2 90^\circ$

Using trigonometric values,

$\sin 60^\circ=\frac{1}{\sqrt2}$

$\cos 90^\circ=0$

$\sec 60^\circ=2$

$\cot 45^\circ=1$

Substitute the value,

$=4(1)^2-(2)^2+(\frac{1}{\sqrt2})^2+(0)^2$

$=4-4+\frac{1}{2}$

$=\frac{1}{2}$

Therefore, $4\cot^2 45^\circ-\sec^2 60^\circ+\sin^2 60^\circ+\cos^2 90^\circ=\frac{1}{2}$

#Learn more

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