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Question

If sinxsiny=12, cosxcosy=32, x, y ϵ (0,π2), then tan (x+y)=___


A

13

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B

14

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C

17

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D

15

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Solution

The correct option is D

15


sinxsiny=12,cosxcosy=322 sin x=sin y,2 cos x=3 cos ytan xtan y=13tan y=3 tan x.
Now, tan(x+y)=tan x+tan y1tan x tan y.
=tan x+3 tan x1tan x(3 tan x)=4 tan x13 tan2 x....(1)
Also, sin y =2 sin x, cosy =23cosx.
sin2 y+cos2 y=14 sin2x+49cos2 x=136 tan2 x+4=9 sec2 x36 tan2 x+4=9(1+tan2 x)27 tan2 x=5tan x=533
tan(x+y)=453311527=45.2712.33=53=15


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