Question

7(tan a-b)=5(tan a+b) then find sin2a /sin2b​

Answer 1

Given: 7 ( tan (a-b) ) = 5 ( tan (a+b) )

To find: sin2a /sin2b​

Solution:

• As we have given that 7 ( tan (a-b) ) = 5 ( tan (a+b) ), so lets convert it in the terms of sin and cos.

                tan (a-b)  /   tan (a+b)  = 5/7

                sin(a-b) x cos(a+b) / cos(a-b) x sin(a+b) = 5/7

• Now, to make it the formula of double angles.

                2 sin(a-b) x cos(a+b) / 2 cos(a-b) x sin(a+b) = 5/7

                ( sin 2a - sin 2b ) / ( sin 2a + sin 2b ) = 5/7

• { sin 2a - sin 2b = 2 sin(a-b) x cos(a+b) and sin 2a + sin 2b = 2 cos(a-b) x sin(a+b) }

• Taking the reciprocal, we get:

                 ( sin 2a + sin 2b ) / ( sin 2a - sin 2b )  = 7/5

• So now, this term is in the form of componendo and dividendo, so we can write it as:

                 sin 2a / sin 2b = 6+1 / 6-1

                 sin 2a / sin 2b = 6/1

Answer:

            So, the value of  sin 2a / sin 2b is 6.