Question

If sin θ + cos θ = √2 cos(90° - θ ) , find cot θ

Answer 1

sin θ + cos θ = √2 cos(90° - θ )

sin θ + cos θ = √2 sin θ

cos θ = √2 sin θ- sin θ

cos θ= (√2-1) sin θ

cos θ/ sin θ= (√2-1)

cot θ= (√2-1).

Answer 2

Hi ,

Here I'm using A instead of theta

sin A + cosA = √2 cos ( 90° - A )

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cos ( 90° - A ) = sin A

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sinA + cosA = √2 sinA

divide each term with sin A , we get

sinA / sinA + cosA/sinA = √2sinA/sinA

1 + cotA = √2

cotA = √2 - 1

I hope this helps you.

:)