Let P ( x 1 , y 1 ) and Q ( x 2 , y 2 ) be two points in the XY-plane whose coordinates satisfy the equation cot 2 ( x + y ) + tan 2 ( x + y ) + y 2 + 2 y − 1 = 0 . The minimum distance betwee

Question

Let P ( x 1 ​ , y 1 ​ ) and Q ( x 2 ​ , y 2 ​ ) be two points in the XY-plane whose coordinates satisfy the equation cot 2 ( x + y ) + tan 2 ( x + y ) + y 2 + 2 y − 1 = 0 . The minimum distance between P and Q is

TestHub · Accepted Answer

[ cot ( x + y ) − tan ( x + y ) ] 2 + ( y + 1 ) 2 = 0 ∴ tan 2 ( x + y ) = 1 and y = − 1 , so x = − 1 + 4 π ​ + 2 kπ ​ . Consecutive points are 2 π ​ apart.

Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

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