Question

sin²0+sin²π/6+sin²π/3+sin²π/2​

Answer 1

Sin π/6 = 1/2

Sin π/3 = √3/2

Sin π/2 = 1

Squaring all and adding

1/4 + 3/4+1

=2

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Answer 2

Given:

sin²0+sin²π/6+sin²π/3+sin²π/2​

To find:

The value of sin²0+sin²π/6+sin²π/3+sin²π/2​

Solution:

The value of sin²0+sin²π/6+sin²π/3+sin²π/2​ is 2.

We can find the value by following the process given below-

We know that the value of π in degrees is taken equivalent to 180°.

So, the required value can be obtained by determining the values of π/6, π/3, and π/2.

We are given the following-

sin²0+sin²π/6+sin²π/3+sin²π/2​

We know that sin 0=0.

Similarly, sin π/6=180/6=30°

sin 30°=1/2

Also, sin π/3=180/3=sin 60°

sin 60°=$\sqrt{3}$/2

Similarly, sin π/2=180/2=sin 90°

sin 90°=1

Using these values, we will determine the required value.

sin²0+sin²π/6+sin²π/3+sin²π/2​= sin²0+$sin^{2} 30$+$sin^{2} 60$+$sin^{2} 90$

=$0^{2}$ +$(1/2)^{2}$+$(\sqrt{3} /2)^{2}$+$1^{2}$

=0+1/4+3/4+1

=4/4+1

=1+1

=2

Therefore, the value of sin²0+sin²π/6+sin²π/3+sin²π/2​ is 2.