Question

if cos²theta- 11 cos Theta +5=0, find the possible value of cos Theta
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Answer 1

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amarnannaware28

amarnannaware28

19.08.2019

Math

Secondary School

+5 pts

Answered

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

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sonuvuce

sonuvuce Ace

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