If = cos( sin−1 ) then prove that
(1 −
2
)+2 − (2 + 1)+1 + (2 −
2
) = 0
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Step-by-step explanation:
If (cosθ+sinθ)=1, prove that (cosθ−sinθ)=±1.
Hard
Solution
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Given
cosθ+sinθ=1
(cosθ+sinθ)
2
=1
2
cos
2
θ+sin
2
θ+2sinθcosθ=1
1+2sinθcosθ=1
2sinθcosθ=0
sinθcosθ=0
Now (cosθ−sinθ)
2
=(cosθ+sinθ)
2
−4sinθcosθ
=1
2
−4×0
=1
(cosθ−sinθ)
2
=1
cosθ−sinθ=±1
∴ Hence proved.
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