Question

if 8 X equal to π so that cos 7 x + cos x is equal to zero

Answer 1

we know,
coaA +cosB= 2cos{(A+B)/2} × cos{(A-B)/2}

so, cos7X + cosX
= 2cos{(7X+X)/2}×cos{(7X-X)/2}
=2cos(8X/2)× cos(3X)
=2cos(π/2)×cos(3X)
=0 {as cos(π/2)=cos90°=0}