Question

Sin11x/4 sinx/4+ sin7x/4 sin3x/4= sin2x sinx

Answer 1

Answer:

To Prove:

sin11x/4 sinx/4+ sin7x/4 sin3x/4= sin2x sinx

LHS

= sin11x/4 sinx/4+ sin7x/4 sin3x/4

= (1/2)[2sin11x/4 sinx/4+ 2sin7x/4 sin3x/4]

= (1/2)[cos{(11x-x)/4}-cos{(11x+x)/4} +cos{(7x-3x)/4}-cos{(7x+3x)/4}]

[Using 2sinAsinB = cos(A-B) - cos(A+B)]

= (1/2)[cos{(5x)/2}-cos(3x) + cos(x)-cos{(5x)/2}]

= (1/2)[cos(x)-cos(3x)]

= (1/2)[2sin{(x+3x)/2} sin{(3x-x)/2}]   (∵ cosA-cosB = 2sin{(A+B)/2} sin{(B-A)/2})

= sin2x sinx

=RHS                          (Proved)

Answer 2

Answer:

May it helps you..

Step-by-step explanation:

Some part of LHS in photo is not coming good due to app restrictions.. So.

In LHS,

1/2 is common from starting to last..

In this question 3 formulas are used..

Firstly take LHS..

Then put the formulas in the question..

Then you find that your RHS be coming..

In last..

LHS =RHS

Hence proved.

Thank you.