Find all the possible solutions for the equations. \tan\theta+\sec\theta=2\cos\theta,\ 0\leq\theta\leq2\pi

enfocarteu7z

enfocarteu7z

Answered question

2022-02-26

Find all the possible solutions for the equations.
tanθ+secθ=2cosθ, 0θ2π

Answer & Explanation

Pooja Copeland

Pooja Copeland

Beginner2022-02-27Added 8 answers

secθ+tanθ=2cosθ=2secθ
secθtanθ=1secθ+tanθ=secθ2
secθ(112)=tanθ
θ=nπ+(1)nπ6 where n is any integer
If n is even =2m, θ=2mπ+π6
As 0θ2π, 02mπ+π62π012m+112
m=0
Similiarly, if n is odd =2m+1, θ=(2m+1)ππ6m=0

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