If cos x-cos y-1-3- sin x-sin y-1-4 then sin x-y-

The correct option is B sin x+sin y/cos x+cos y=3/4 ⇒2sin(x+y/2)cos(x y/2)/2cos(x+y/2)cos(x y/2)=3/4 ⇒ tan ( x+y/2 )=3/4 ⇒ sin(x+y)=2.(3/4)/1+(9/16)=24/25 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Sum of n Terms in GP

If cos x+cos ...

Question

If cos x +cosy = $\frac{1}{3}$ , sin x + sin y = $\frac{1}{4}$ then sin (x + y) =

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
$\frac{s i n x + s i n y}{c o s x + c o s y} = \frac{3}{4} \Rightarrow \frac{2 sin (\frac{x + y}{2}) cos (\frac{x - y}{2})}{2 cos (\frac{x + y}{2}) cos (\frac{x - y}{2})} = \frac{3}{4} \Rightarrow t a n (\frac{x + y}{2}) = \frac{3}{4} \Rightarrow s i n (x + y) = \frac{2. (\frac{3}{4})}{1 + (\frac{9}{16})} = \frac{24}{25}$

Suggest Corrections

Similar questions

Q. I:

cos x + cos y = \frac{1}{3}, sin x + sin y = \frac{1}{4}

, then

cos (x + y) = \frac{- 7}{25}

.
II.

sin x + sin y = \frac{1}{4}, sin x - sin y = \frac{1}{5}

, then

4 cot (\frac{x - y}{2}) = 5 cot (\frac{x + y}{2})

If sin x+siny = $\frac{1}{2}$ and cosx+cosy = 1, then tan (x+y) = ……..

If sin x – sin y = $\frac{1}{2}$ and cos x – cos y = 1 then tan (x + y)=

Q. If

sin x + sin y = \frac{1}{2}

and

cos x + cos y = 1

, then

tan (x + y) =

____

Q. If

x

and

y

are acute angles such that

cos x + cos y = \frac{3}{2}

and

sin x + sin y = \frac{3}{4}

then

sin (x + y) =

Join BYJU'S Learning Program

If cos x +cosy = 13, sin x + sin y = 14 then sin (x + y) =

The correct option is B sin x+sin ycos x+cos y=34⇒2sin(x+y2)cos(x−y2)2cos(x+y2)cos(x−y2)=34⇒tan(x+y2)=34⇒sin(x+y)=2.(34)1+(916)=2425

If cos x +cosy = $\frac{1}{3}$ , sin x + sin y = $\frac{1}{4}$ then sin (x + y) =