find-the-solution-set-of-the-equation-sec-3-sec-

Question Number 117497 by bemath last updated on 12/Oct/20

find the solution set of the

equation \sec 3 θ = \sec θ

Answered by Dwaipayan Shikari last updated on 12/Oct/20

\frac{1}{c o s 3 θ} = \frac{1}{c o s θ}

c o s 3 θ = c o s θ

4 {c o s}^{3} θ - 3 c o s θ = c o s θ

{c o s}^{3} θ = c o s θ

c o s θ ({c o s}^{2} θ - 1) = 0

c o s θ = 0

{c o s}^{2} θ - 1 = 0

θ = k π + \frac{π}{2}

c o s θ = 1 o r c o s θ = - 1

θ = 2 k π θ = 2 π k + π (k \in Z)