Question

If sinθ + cosθ = √2cosθ, (θ ≠ 90o) then the value of tanθ is

Answer 1

value of tanθ = √2 - 1

it is given that, sinθ + cosθ = √2cosθ

we have to find tanθ = ?

sinθ + cosθ = √2cosθ

dividing by cosθ both sides,

sinθ/cosθ + cosθ/cosθ = √2cosθ/cosθ

⇒sinθ/cosθ + 1 = √2

from trigonometric identities,

⇒tanθ + 1 = √2

⇒tanθ = √2 - 1

hence, value of tanθ = √2 - 1

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