Question

sin theta+cos theta=m then sin theta-cos theta=

Answer 1

(sin theta + cos theta )^2 = m^2

1+2sin theta cos theta = m^2

let sin theta - cos theta = x

squaring both side.

1-2sin theta cos theta = x^2

1- (m^2-1) = x^2

x = sqrt(2-m^2)

Answer 2

Sint+cost=m
=>(sint+cost) ^2=m^2
=>(sint) ^2+(cost) ^2+2×sint×cost=m^2
=>2sintcost=m^2-1
=>4sintcost=2m^2-2

(sint+cost) ^2-4sintcost=m^2-2m^2+2
=>(sint-cost) ^2=2-m^2
=>sint-cost=√(2-m^2)