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Question
If sinθ + cosθ = 1, then find the general value of θ.
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Solution
Given, sinθ + cosθ = 1
On dividing both the sides by `sqrt2`,
`sintheta/sqrt2 + costheta/sqrt2 = 1/sqrt2`
⇒ `cos(theta - pi/4) = cos pi/4`
⇒ `theta - pi/4 = pi/4`
We know that, θ = 2nπ ± α when cosθ = cosα
⇒ `theta - pi/4 = 2npi ± pi/4, n ∈ z`
⇒ `theta = 2npi ± pi/4 + pi/4`
Taking the positive sign,
⇒ `theta = 2npi + pi/4 + pi/4`
⇒ `theta = 2npi + pi/2`
Taking the Negative sign,
⇒ `theta = 2npi - pi/4 + pi/4`
⇒ θ = 2nπ, n ∈ z
So, the general value is `theta = 2npi + pi/2` and θ = 2nπ.
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