Question

If sin theta +cos theta = a , sin theta - cos theta =b , prove that a^2+ b^2 = 2

Answer 1

Given-sinѲ+cosѲ=a

sinѲ-cosѲ=b

To prove-a^2+b^2=2

Solution-

L.H.S

=(sinѲ+cosѲ)^2+(sinѲ-cosѲ)^2

=sin^2Ѳ+cos^2Ѳ+2sinѲcosѲ+sin^2Ѳ+cos^2Ѳ-2sinѲcosѲ

=1+1 [sin^2Ѳ+cos^2Ѳ=1]

=2

=R.H.S

Hence proved

Answer 2

Answer:

L.H.S=R.H.S

Step-by-step explanation:

L.H.S

=(sinѲ+cosѲ)^2+(sinѲ-cosѲ)^2

=sin^2Ѳ+cos^2Ѳ+2sinѲcosѲ+sin^2Ѳ+cos^2Ѳ-2sinѲcosѲ

=1+1 [sin^2Ѳ+cos^2Ѳ=1]

=2

=R.H.S

Hence proved