If sin theta +cos theta = a , sin theta - cos theta =b , prove that a^2+ b^2 = 2
Answers
Answered by
5
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
Answered by
1
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
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