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1. if x-y= Π/4 and cotx +coty=2;find smallest +ve angles of x and y.

1. if x-y= Π/4 and cotx +coty=2;find smallest +ve angles of x and y.

Grade:11

1 Answers

Abhi
13 Points
4 years ago
We have, x − y = π4⇒x = π/4 + y⇒cot x = cot( π/4 + y)⇒ cot x = cot(π/4) . cot y − 1cot(π/4) + cot y⇒cot x = cot y − 11 + cot y .......(1)Now, cot x + cot y = 2⇒cot x= 2 − cot y .....(2)From (1) and (2), we get cot y − 11 + cot y = 2 − cot y⇒2 cot y + 2 − cot2y − cot y − cot y + 1 = 0⇒cot2y = 3⇒cot y = 3√⇒cot y = cot (π/3)⇒y = π6Now, x − y = π/4⇒x = π/4 + π/6⇒x = 3π + 2π/12 = 5π/12

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