Q54 of 268 Page 4

If cosec A + cot A = 5, find the value of cos A.

cosec A + cot A = 5

⇒ cotA = 5 – cosecA


Squaring both the sides, we get


⇒ cot2 A =(5 – cosecA)2


⇒ cot2 A = 25 + cosec2A – 10cosec A


⇒ cosec2 A – 1 = 25 + cosec2A – 10cosec A [∵ 1+ cot2 A = cosec2 A]


⇒ –1 – 25 = –10cosecA


⇒ – 26 = –10cosec A





Now, cosec A + cot A = 5








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