Question

2 cos square theta-11cos theta+5=0 find possible value of cos theta​

Answer 1

Answer:

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

Step-by-step explanation:

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

$2cos^2\theta-10cos\theta-cos\theta+5=0$

$2cos\theta(cos\theta-5)-1(cos\theta-5)=0$

$(2cos\theta-1)(cos\theta-5)=0$

$\implies\:cos\theta=5,\frac{1}{2}$

$cos\theta=5\:\text{which is not possible}$

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

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

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

Answer 2

Answer: The value of  $cos\theta =\dfrac{1}{2}$

Step-by-step explanation:

To find : Value of cos∅ for given equation

$2 cos^2\theta -11 cos \theta + 5$ ------(i)

Let cos∅ = y

∴ (i) becomes the quadratic  equation  $2y^2-11y + 5$

Now

$2y^2-11y+ 5 =0\\\\\Rightarrow 2y^2 -10y-y+5=0\\\\\Rightarrow 2y(y-5) -1(y-5)= 0\\\\\Rightarrow (2y-1)(y-5)=0 \\\\\Rightarrow2y-1= 0 \text { or } y-5= 0\\\\\Rightarrow y= \dfrac{1}{2} \text { or } y=5 ( \text {which is not possible)}$

Hence, the value of  $cos\theta =\dfrac{1}{2}$