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Question
Evaluate: `(cot^2 41°)/(tan^2 49°) - 2 (sin^2 75°)/(cos^2 15°)`
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Solution
`(cot^2 41°)/(tan^2 49°) - 2 (sin^2 75°)/(cos^2 15°)`
tan(49°) = cot(41°)
(because 49° + 41° = 90°)
`(cot^2 41°)/(tan^2 49°) = (cot^2 41°)/(cot41°)^2 = 1`
`(sin^2 75°)/(cos^2 15°)`
sin75° = cos15°
`(sin^2 75°)/(cos^2 15°) = (cos15°)^2/(cos15°)^2 = 1`
1 − 2(1) = 1 − 2
= −1
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