Question

If sinax +cosbx = 1 then find the value of x

Answer 1

• Subtract one of the terms from both sides. 
• You get sin(ax)-sin(bx)=0 
• Use identity sinA - sinB =2sin[(A-B)/2]cos[(a+b)/2]
• In this case A=ax and B=bx
• Then either sin[(a-b)x/2]=0 or cos[(a+b)x/2]=0
• cos(ax)=cos(bx)
• for this identity a and b would be equallcos(ax)=cos(bx)

• cos(ax)=cos(bx)