Question

If 2 cos theta-11costheta +5=0 then the permissible value of cos theta is
d) 1
a) 5
2​

Answer 1

Answer:

cosθ = 1/2

Step-by-step explanation:

Correct Question :-

If 2cos^2θ − 11cosθ + 5 = 0 then find possible values of cosθ.

Given,

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

To Find :-

Value of 'cosθ'.

Solution :-

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

We can write "-11cosθ" as :  -10cosθ - cosθ

→ 2cos^2θ - 10cosθ - cosθ + 5 = 0

Taking '2cosθ' common :-

2cosθ(cosθ - 5) - 1 ( cosθ - 5) = 0

Taking 'cosθ - 5' common :-

(cosθ - 5)(2cosθ - 1) = 0

Equating both terms to zero :

cosθ - 5 = 0 , 2cosθ - 1 = 0

cosθ = 5 , 2cosθ = 1

cosθ ≠ 5 , cosθ = 1/2

∴ cosθ ≠ 5 because  - 1 ≤ cosθ ≤ 1

→ cosθ = 1/2

Know More :-

1) - 1 ≤ sinθ ≤ 1

2) - 1 ≤ cosθ ≤ 1

3)  secθ ≤ -1 and secθ ≥ 1

4)  cscθ ≤ -1 and cscθ ≥ 1