If sin⁡x+cos⁡y=1/3 and cos⁡x+sin⁡y=3/4, then the value of tan⁡(x-y)/2 is equal to

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Correct answer: (C) -5/13. sin⁡x+sin⁡(π)/2-y=1/3 ⇒2sin⁡(π)/4+(x-y)/2cos⁡(x+y)/2-(π)/4=1/3 cos⁡x+cos⁡(π)/2-y=3/4 ⇒2cos⁡(π)/4+(x-y)/2cos⁡(x+y)/2-(π)/4=3/4 On dividing we get, tan⁡(π)/4+(x-y)/2=4/9 ⇒(1+tan⁡x-y)/21-tan⁡(x-y)/2=4/9 Using componendo and dividendo, we get 2/(2tan⁡x-y2)=13/(-5)⇒tan⁡(x-y)/2=-5/13

If $\sin x + \cos y = \frac{1}{3}$ and $\cos x + \sin y = \frac{3}{4}$ , then the value of $\tan (\frac{x - y}{2})$ is equal to

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If sin⁡x+cos⁡y=13 and cos⁡x+sin⁡y=34, then the value of tan⁡x-y2 is equal to

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If $\sin x + \cos y = \frac{1}{3}$ and $\cos x + \sin y = \frac{3}{4}$ , then the value of $\tan (\frac{x - y}{2})$ is equal to