Q.51. Trigonometry

Question 51.
Find the value of cot15° + cot75° + cot135° + cosec30° without using the value of 15° of any trigonometric function.

Answer 51.
cot15° + cot75° + cot135° + cosec30°
= cot15° + cot(90°-15°) + cot(90°+45°) + 1/sin30°
= cot15° + tan15° - tan45° + 1/(1/2)
= cos15°/sin15° + sin15°/cos15° - 1 + 2
= (cos^2 15° + sin^2 15°)/sin15°cos15° + 1
= 2/2sin15°cos15° + 1
= 2/sin30° + 1
= 2/(1/2) + 1
= 4 + 1
= 5.

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