Math, asked by Akhil2922, 1 year ago

sinx +siny =a, cosx +cosy =b find tan(x-y/2)

Answers

Answered by Shubhendu8898
44
Hi ...dear...here is your answer..

... Given,
sinx +siny =a,
and
cosx +cosy =b....
...
..
we can apply the formula of cosC + cosD
and sinC + sinD....
let's start....

..see picture!!!
hope it helped you..
Regards Brainly Star Community
#shubhendu
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Answered by pinquancaro
25

Answer:

The value of \tan(\frac{x+y}{2})=\frac{a}{b}

Step-by-step explanation:

Given : \sin x +\sin y =a, \cos x +\cos y =b

To find : The value of \tan(\frac{x+y}{2})

Solution :

\sin x +\sin y =a

We know, \sin x+\sin y=2\sin(\frac{x+y}{2})\cos(\frac{x-y}{2})

2\sin(\frac{x+y}{2})\cos(\frac{x-y}{2})=a.....(1)

 \cos x +\cos y =b

We know,  \cos x +\cos y =2\cos(\frac{x+y}{2})\cos(\frac{x-y}{2})

2\cos(\frac{x+y}{2})\cos(\frac{x-y}{2})=b ....(2)

Divide (1) and (2),

\frac{2\sin(\frac{x+y}{2})\cos(\frac{x-y}{2})}{2\cos(\frac{x+y}{2})\cos(\frac{x-y}{2})}=\frac{a}{b}

\tan(\frac{x+y}{2})=\frac{a}{b}

Therefore, The value of \tan(\frac{x+y}{2})=\frac{a}{b}

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