Question

if sin a + cos a = root 2 then find value of cot a

Answer 1

Given Equation is (sina + cosa) = root 2.

On squaring both sides, we get

(sina + cosa)^2 = (root2)^2

sin^2a + cos^2a + 2sinacosa = 2

1 + 2sinacosa = 2

2sinacosa = 1

sin2a = 1

sin2a = sin 90

2a = 90

a = 45.


Therefore,

cota = cot(45)

        = 1.


Therefore the value is 1.


Hope this helps!