Home
Class 12
MATHS
If sin x + sin y =(1)/(2) andcosx+cosy=1...

If sin x + sin y `=(1)/(2) andcosx+cosy=1`, then tan (x+y) is equal to

A

`(-8)/(3)`

B

`(8)/(3)`

C

`(4)/(3)`

D

`-(3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have , sin x +sin y `=(1)/(2)`
`rArr2sin((x+y)/(2))cos((x-y)/(2))=(1)/(2)` …(i)
and cos x + cos y =1
`rArr2cos((x+y)/(2))cos((x-y)/(2))=1` …(ii)
On dividing Eq . (i) by Eq . (ii) , we get
`tan((x+y)/(2))=(1)/(2)`
Now , `tan(x+y)=(2tan((x+y)/(2)))/(1-tan^(2)((x+y)/(2)))=(2xx(1)/(2))/(1((1)/(2))^(2))=(4)/(3)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If cosx=3cosy , then 2tan.(y-x)/(2) is equal to

If sin x+sin y=a and cos x+cos y=b, then tan((x+y)/2 ' is equal to

If sin x + sin y = (7) / (5) and cos x + cos y = (1) / (5) then sin (x + y) equal to

" 1.If sin x+sin y=(1)/(4),cos x+cos y=(1)/(3) then tan((x+y)/(2))=

If sin x + cos y = (1) / (3) and cos x + sin y = (3) / (4) then tan ((xy) / (2)) =

If (sin (x+y))/( sin(x-y))=(a+b)/(a-b) , then (tan x)/( tan y) is equal to

If sin x cos y=(1)/(4) and 3tan x=4tan y then sin(x-y)=