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Evaluate the Following Sin2 30° + Sin2 45° + Sin2 60° + Sin2 90° - Mathematics

Evaluate the following

sin2 30° + sin2 45° + sin2 60° + sin2 90°

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Solution

sin2 30° + sin2 45° + sin2 60° + sin2 90°  .....(1)

`sin 30^@ = 1/2     sin 45^@ = 1/sqrt2`

`sin 60^@ = sqrt3/2   sin 90^@ = 1`

By substituting above values in (i), we get

`= [1/2]^2 + [1/sqrt2]^2 + [sqrt3/2]^2 + [1]^2`

`= 1/4 + 1/2 + 3/4 + 1 => (1 + 3)/4 + (1 + 2)/2`

`=> 1 + 3/2 = (2 + 3)/2 = 5/2`

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 10 Trigonometric Ratios
Exercise 10.2 | Q 4 | Page 41
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