Question

If sin(a+b)=√3/2 and cos(a-b)=√3/2 then find a and b.

Answer 1

hope this will be useful to you

Answer 2

Answer:

a = 45 and b = 15

Step-by-step explanation:

Given,

sin(a+b) =  $\frac{\sqrt{3} }{2}$

cos(a-b) =  $\frac{\sqrt{3} }{2}$

To find,

The value of 'a' and 'b'

Solution:

Recall the concepts

sin 60 =  $\frac{\sqrt{3} }{2}$ and cos 30=  $\frac{\sqrt{3} }{2}$

Sin(a+b)  =  $\frac{\sqrt{3} }{2}$  = sin 60

a+b = 60---------------(1)

cos(a-b) =  $\frac{\sqrt{3} }{2}$ = cos 30

a-b = 30 ---------------(2)

adding (1) and(2) we get

2a = 90

a = 45

Substitute the value of 'a' in equation (1) we get

45 +b = 60

b = 15

∴a = 45 and b = 15

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