Question

If sinθ+cosθ=√2cos(90°-θ), find cotθ.

Answer 1

Step-by-step explanation:

here's your answer...

Answer 2

Answer:

√ 2 - 1

Step-by-step explanation:

Given :

sin Ф + cos Ф = ( √ 2 ) cos ( 90 - Ф )

We are asked to find value of cot Ф :

We know :

cos ( 90 - Ф ) = sin Ф

sin Ф + cos Ф = ( √ 2 ) sin Ф

Dividing whole equation by sin Ф we get :

sin Ф /  sin Ф + cos Ф/  sin Ф = ( √ 2 ) sin Ф /  sin Ф

1 +  cos Ф / sin Ф = ( √ 2 )

cos Ф / sin Ф = √ 2 - 1

But we know :

cot Ф = cos Ф/ sin Ф

= > cot Ф  = √ 2 - 1

Therefore the value of cot Ф is √ 2 - 1 .