If the sum of all values of satisfying the system x+ y+ x y=5 (x+y)=4 x y is

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

If the sum of all values of xx satisfying the system tan⁡x+tan⁡y+tan⁡xtan⁡y=5\tan x+\tan y+\tan x\tan y=5 sin⁡(x+y)=4cos⁡xcos⁡y\sin(x+y)=4\cos x\cos y is kπ2\frac{k\pi}{2}, where x∈(0,π2)x\in\left(0,\frac{\pi}{2}\right), find the value of kk.

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