Question

I want solution...please help me

Answer 1

sin(θ) + cos(θ) = 1

Divide both sides by √2:

1/√2 sin(θ) + 1/√2 cos(θ) = 1/√2

We do this because sin(x) = cos(x) = 1/√2 for x = π/4, and this lets us condense the left side using either of the following angle sum identities:

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

cos(x - y) = cos(x) cos(y) - sin(x) sin(y)

Depending on which identity you choose, we get either

1/√2 sin(θ) + 1/√2 cos(θ) = sin(θ + π/4)

or

1/√2 sin(θ) + 1/√2 cos(θ) = cos(θ - π/4)

Let's stick with the first equation, so that

sin(θ + π/4) = 1/√2

θ + π/4 = π/4 + 2nπ   or   θ + π/4 = 3π/4 + 2nπ

(where n is any integer)

θ = 2nπ   or   θ = π/2 + 2nπ

We get only one solution from the second solution set in the interval 0 < θ < 2π when n = 0, which gives θ = π/2.