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Evaluate: Cot 2 41 ° Tan 2 49 ° − 2 Sin 2 75 ° Cos 2 15 ° - Mathematics

Sum

Evaluate: `(cot^2 41°)/(tan^2 49°) - 2 (sin^2 75°)/(cos^2 15°)`

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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

Concept: Trigonometric Ratios of Complementary Angles
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 25 Complementary Angles
Exercise 25 | Q 6.7 | Page 310
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