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Question
Evaluate: `(cot^2 41°)/(tan^2 49°) - 2 (sin^2 75°)/(cos^2 15°)`
Solution 1
`(cot^2 41°)/(tan^2 49°) - 2 (sin^2 75°)/(cos^2 15°)`
= `[cot(90°- 49°)]^2/(tan^2 49°)- 2[sin(90° - 15°)]^2/(cos^2 15°)`
= `(tan^2 49°)/(tan^2 59°) - 2 (cos^2 15°)/(cos^2 15°)`
= 1 - 2
= -1
Solution 2
`(cot^2 41°)/(tan^2 49°) - 2 (sin^2 75°)/(cos^2 15°)`
= `[cot(90°- 49°)]^2/(tan^2 49°)- 2[sin(90° - 15°)]^2/(cos^2 15°)`
= `(tan^2 49°)/(tan^2 49°) - 2 (cos^2 15°)/(cos^2 15°)`
= 1 - 2
= -1
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