If c o s x - s i n x = - 5 4 , where π 2 x 3 π 4 , then c o t x 2 is equal to

Question

If c o s x - s i n x = - 5 4 , where π 2 x 3 π 4 , then c o t x 2 is equal to, 4 - 7 9, 8, - 8, 4 + 7 9

MARKS App · Accepted Answer

Given, 4 cos ⁡ x - sin ⁡ x = - 5 4 1 - t a n 2 x 2 1 + t a n 2 x 2 - 2 tan ⁡ x 2 1 + t a n 2 x 2 =- 5 ⇒ 4 - 4 tan 2 ⁡ x 2 - 8 tan ⁡ x 2 = - 5 - 5 tan 2 ⁡ x 2 ⇒ t a n 2 x 2 - 8 tan ⁡ x 2 + 9 = 0 ⇒ 9 cot 2 ⁡ x 2 - 8 cot ⁡ x 2 + 1 = 0 ⇒ c o t x 2 = 4 ± 7 9 Since, π 4 x 2 3 π 8 ⇒ 2 - 1 c o t x 2 1 ⇒ c o t x 2 = 4 + 7 9

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