Sin square 30°+sin square 45°+sin square 60°
Answers
Answer:
sin
2
30+sin
2
45+sin
2
60+sin
2
90=
2
5
Step-by-step explanation:
Given : Expression \sin^2 30+\sin^2 45+\sin^2 60+\sin^2 90sin
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 90sin
2
30+sin
2
45+sin
2
60+sin
2
90
Using trigonometric values,
\sin 30=\frac{1}{2}sin30=
2
1
\sin 45=\frac{1}{\sqrt2}sin45=
2
1
\sin 60=\frac{\sqrt3}{2}sin60=
2
3
\sin 90=1sin90=1
Substitute the values,
=(\frac{1}{2})^2+(\frac{1}{\sqrt2})^2+(\frac{\sqrt3}{2})^2+(1)^2=(
2
1
)
2
+(
2
1
)
2
+(
2
3
)
2
+(1)
2
=\frac{1}{4}+\frac{1}{2}+\frac{3}{4}+1=
4
1
+
2
1
+
4
3
+1
=\frac{1+2+3+4}{4}=
4
1+2+3+4
=\frac{10}{4}=
4
10
=\frac{5}{2}=
2
5
Therefore, \sin^2 30+\sin^2 45+\sin^2 60+\sin^2 90=\frac{5}{2}sin
2
30+sin
2
45+sin
2
60+sin
2
90=
2
5
#Learn more
sin 30 cos 30 + cos 30 sin 60 = sin 90