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Without using trigonometric tables evaluate the following: (i) sin^2 25º + sin^2 65º - Mathematics

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Sum

Without using trigonometric tables evaluate the following:

`(i) sin^2 25º + sin^2 65º `

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Solution

(i) We have,

`sin^2 25º + sin^2 65º = sin^2 (90º – 65º) + sin^2 65º`

`= cos265º + sin265º = 1`

[∵ sin (90º – θ) = cos θ]

(ii) We have,

`cos^2 13º– sin^2 77º = cos^2 (90º – 77º) – sin^2 77º`

`= sin^2 77º – sin^2 77º = 0`

[∵ cos (90º – θ) = sin θ]

Concept: Trigonometric Ratios of Complementary Angles
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