Question

Prove that 2(1 - 2 sin^2 7a)sin 3a = sin 17a - sin 11a

Answer 1

Step-by-step explanation:

2(1-2sin^2 7a ) sin3a = sin17a - sin11a

LHS = (1-2sin^2 7a) sin3a

we know that cos2a = 1-2sin^2a

so 1-2 sin^2 7a = cos(2*7a) = cos14a

so LHS = cos14a * sin3a

now multiplying and dividing 2

= (2cos14a * sin3a) * 1/2

we know that 2 cosa sinb = sin(a+b) /2 - sin(a-b)/2

= sin(14a+3a) /2 - sin(14a-3a) /2

= sin17a - sin11a = RHS

hence proved.

hope u understood it