Question

4 cos square 60°+4 sin square 45°-sin square 30°​

Answer 1

cos 60° = 1/2

sin 45° = 1/√2

sin 30° =1/2

Now, according to question

4×1/4 + 4 × 1/2 - 1/4.

1 + 2 -1/4

=11/4

Answer 2

$4\cos^2(60^\circ)+4\sin^2(45^\circ)-\sin^2(30^\circ)=\frac{19}{4}$

Step-by-step explanation:

Given : Expression  $4\cos^2(60^\circ)+4\sin^2(45^\circ)-\sin^2(30^\circ)$

To find : Simplify the expression ?

Solution :

Expression  $4\cos^2(60^\circ)+4\sin^2(45^\circ)-\sin^2(30^\circ)$

Using trigonometric values,

$\cos 60=\frac{\sqrt3}{2},\ \sin (45)=\frac{1}{\sqrt2},\ \sin(30)=\frac{1}{2}$

Substitute the values in the expression,

$=4(\frac{\sqrt3}{2})^2+4(\frac{1}{\sqrt2})^2-(\frac{1}{2})^2$

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

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

$=5-\frac{1}{4}$

$=\frac{20-1}{4}$

$=\frac{19}{4}$

Therefore, $4\cos^2(60^\circ)+4\sin^2(45^\circ)-\sin^2(30^\circ)=\frac{19}{4}$

#Learn more

4 cos square 60 degree + sec square 30 degree minus 2 sin square 45 degree upon sin square 60 degree + cos square 45 degree

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