Question

If Sin theta + costheta=√2cos(90-theta) then cott theta is equal to​

Answer 1

Hi baby

sinθ+cosθ=√2cos(90- θ)

= sinθ + cosθ = √2sinθ

= (sinθ + cosθ)/sinθ = √2sinθ/sinθ [dividing both sides by sinθ ]

= 1 + cotθ = √2

= cotθ = √2-1

Answer 2

sin theta + cos theta = √2 cos(90°-theta)

sin theta + cos theta = √2 sin theta

[ SQUARE ON BOTH THE SIDES]

sin^2 theta + cos^2 theta = (√2 sin theta)^2

[Sin^2 theta + Cos^2 theta = 1]

1 = 2 sin^2 theta

1/2 = sin^2 theta

1/√2 = sin theta

SIN theta = 1/√2

SIN 45° = 1/√2

so theta = 45°

Cot theta = Cot 45° = 1