Question

sin^2 1°+sin^2 2°+..................+sin^2 90° =?
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Answer 1

Given:

A trigonometric expression, sin^2 1°+sin^2 2°+...+sin^2 90°.

To Find:

The value of the trigonometric expression.

Solution:

The given question can be solved by using the concepts of trigonometry.

1. The given expression is sin^2 1°+sin^2 2°+...+sin^2 90°,

2. According to the properties of trigonometry,

=> [sin(90-x)] = cosx,

=> sin^2 x + cos^2 x = 1,

3. The given expression can also be written as,

=> sin^2 1°+ cos^2 1° + sin^2 2° + cos^2 2° + ... + sin^2 90°.

=> 1 + 1 + 1 + 1 + 1 +(  45 times) + sin^ 45°, ( Since Sin^2 x + Cos^2 x = 1)

=> 45 + 1/2, ( Sin^2 45° = 1/2),

=> 45.5.

Therefore, the value of sin^2 1°+sin^2 2°+...+sin^2 90° is 45.5.