If $2 \cos ^2 \theta-5 \cos \theta+2=0,0^{\circ}<\theta<90^{\circ}$, then the value of $(\sec \theta+\tan \theta)$ is:
Answer & explanation
Correct answer: option 1
We are given :-
2cos²θ - 5cosθ + 2 = 0
2cos²θ - 4cosθ - cosθ + 2 = 0
2cosθ ( cosθ - 2 ) - 1 ( cosθ - 2 ) = 0
( 2cosθ - 1 ) . ( cosθ - 2 ) = 0
Either ( 2cosθ - 1 ) = 0 or ( cosθ - 2 ) = 0
( cosθ - 2 ) = 0 is not possible
So, ( 2cosθ - 1 ) = 0
cosθ = \(\frac{1}{2}\)
{ We know, cos60º = \(\frac{1}{2}\) }
So, θ = 60º
Now,
secθ + tanθ
= sec60º + tan 60º
= 2 + √3