The expression sinxcospi7cosxsinpi7 is equal to acosxpi7 bsi

The expression sin(x)cos(pi/7)-cos(x)sin(pi/7) is equal to:

a)cos(x+pi/7)

b)sin(x-pi/7)

c)neither

Solution

We have given The expression sin(x)cos(pi/7)-cos(x)sin(pi/7)

using the formula sinAcosB-cosAsinB=sin(A-B)

let A=x,B=pi/7

sin(x)cos(pi/7)-cos(x)sin(pi/7) =sin(x-pi/7)

answer is b) sin(x-pi/7)