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Ritu Chopra

· started a discussion

· 1 Months ago

required Solution (Question: 209669.0 )

give solution

Question:
If sin x + sin y = a and cos x + cos y =  b, find the value of tan \(\cfrac{x + y}{2}\) . 
Options:
A) \(\cfrac{a}{b}\)
B) \(\cfrac{b}{a}\)
C) \(\cfrac{4}{a^2 + b^2}\)
D) \(\cfrac{4}{a^2 - b^2}\)
Solution:
Ans: (a)


Knowledge Expert

· commented

· 1 Months ago

Dear Student
Please refer below solution,

As we know , cosX + cosY = 2cos[ (X + Y) / 2 ] cos[ (X - Y) / 2 ]

sinX + sinY = 2sin[ (X + Y) / 2 ] cos[ (X - Y) / 2 ]

Therefore using it , 2sin[ (X + Y) / 2 ] cos[ (X - Y) / 2 ] = a -------1 )
2cos[ (X + Y) / 2 ] cos[ (X - Y) / 2 ] = b -------2)

Divide eqn 1) by eqn 2) , we get
2sin (X + Y) / 2cos(X + Y) = a/b
Therefore, Tan (X + Y) = a/b
Hope you understood
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