Question

If = cos( sin−1 ) then prove that

(1 −

2

)+2 − (2 + 1)+1 + (2 −

2

) = 0​

Answer 1

Step-by-step explanation:

If (cosθ+sinθ)=1, prove that (cosθ−sinθ)=±1.

Hard

Solution

verified

Verified by Toppr

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.