Question

sin 7 A - sin A
__________ =cos 4 A sec5A
sin 8A -sin 2A​

Answer 1

used to formula sin c+sin d

Answer 2

LHS=(sin7A-sinA)/(sin8A-sin2A)

     =(2cos((7A+A)/2)sin((sin7A-A)/2)/(2cos((8A+2A)/2)sin((8A-2A)/2)

    =(2cos4Asin3A)/(2cos5Asin3A)

    =cos4A* (1/cos5A)

     =cos4Asec5A=RHS

PROVED