Question

If cot A +sinA =√2 proof that cotA=√2+1​

Answer 1

Explanation:

Given Sin A + cos A = root 2 sin(90 - A)

Sin A + cos A = root 2 cos A

Squaring on both sides, we get

(Sin A + cos A)^2 = (root 2 cos A)^2

sin^2 A + cos ^2 A + 2 sin A cos A = 2 cos^2 A

1 + 2 Sin A cos A = 2 cos^2 A

2 Sin A cos A = 2 cos ^2 A - 1

Sin 2A = cos 2 A

Tan 2 A = 1

2A = 45

A = 22.5.

Multiply with cot on both sides, we get

Cot A = cot 22.5

Cot A = root 2 + 1.