Question

If sin a+b =1 , tan a-b =1/root3 find a and b

Answer 1

Answer:

$\sin(a + b) = 1$

$sin(a + b) = \sin(90)$

a + b = 90

a = 90 - b ..............(1)

$\tan(a - b) = \frac{1}{ \sqrt{3} }$

$\tan(a - b) = \tan(30)$

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

now substituting the value of a in equation (2)

=> (90 - b )- b = 30

=> 90 - b - b = 30

=> 90 -2b = 30

=> 90 - 30 = 2b

=> 2b = 60

=> b = 60/2

=> b = 30

=> a= 90 - b

=> a = 90 - 30

=> a = 60

a = 60 and b = 30