Question

Sin square 30 + sin square 45 + sin square 60 + sin square 90

Answer 1

See the attachment below

Answer 2

$\sin^2 30+\sin^2 45+\sin^2 60+\sin^2 90=\frac{5}{2}$

Step-by-step explanation:

Given : Expression $\sin^2 30+\sin^2 45+\sin^2 60+\sin^2 90$

To find : The value of expression ?

Solution :

Expression $\sin^2 30+\sin^2 45+\sin^2 60+\sin^2 90$

Using trigonometric values,

$\sin 30=\frac{1}{2}$

$\sin 45=\frac{1}{\sqrt2}$

$\sin 60=\frac{\sqrt3}{2}$

$\sin 90=1$

Substitute the values,

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

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

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

$=\frac{10}{4}$

$=\frac{5}{2}$

Therefore, $\sin^2 30+\sin^2 45+\sin^2 60+\sin^2 90=\frac{5}{2}$

#Learn more

sin 30 cos 30 + cos 30 sin 60 = sin 90​

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