Question

Find the numerical value of..... cot15+cot75+cot135-cosec30
along with explanation
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Answer 1

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.