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Question
Evaluate: `((sin 77°)/(cos 13°))^2 + ((cos 77°)/(sin 13°))^2 - 2 cos^2 45°`
Sum
Solution
`((sin 77°)/(cos 13°))^2 + ((cos 77°)/(sin 13°))^2 - 2 cos^2 45°`
= `(sin(90° - 13°)/(cos 13°))^2 + (cos(90° - 13°)/(sin 13°))^2 - 2 (cos 45°)^2`
= `((cos 13°)/(cos 13°))^2 + ((sin 13°)/(sin 13°))^2 - 2 (1/sqrt(2))^2`
= `(1)^2 + (1)^2 - 2 xx (1)/(2)`
= 1 + 1 - 1
= 1
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Complementary Angles for Sine ( Sin ) and Cosine ( Cos )
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