Question

if 2 cos square theta - 11 cos theta + 5 equal to zero then find possible value of cos theta​

Answer 1

Answer:

The value of cosθ is 1/2

Step-by-step explanation:

Given

$2\cos^2\theta-11\cos\theta+5=0$

Let cosθ = t

Then

$2t^2-11t+5=0$

$\implies 2t^2-10t-t+5=0$

$\implies 2t(t-5)-1(t-5)=0$

$\implies (2t-1)(t-5)=0$

$\implies t=1/2, 5$

$\implies \cos\theta=1/2, 5$

But maximum value of cosθ is 1

Therefore, it can never be equal to 5

Thus,

$\cos\theta=\frac{1}{2}=\cos\frac{\pi}{3}$

$\implies \theta=2n\pi\pm\frac{\pi}{3}$

where n is an integer

The value of cosθ is 1/2