JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Trigonometric Equations

3 (cos^{2} x) = (3 - 1) cos x + 1

, the number of solutions of the given equation when

x \in [0, \frac{π}{2}]

is ____

Answer: 1

Solution

Put

t = cos x

, so the equation becomes

3 t^{2} - (3 - 1) t - 1 = 0

which factorises as

(t - 1) (3 t + 1) = 0

, giving

t = 1

t = - \frac{1}{3}

.
For

x \in [0, \frac{π}{2}]

the value of

cos x

lies in

[0, 1]

, so the negative root is never attained, while

t = 1

gives the single value

x = 0

.
The equation has

1

solution in the given interval.

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Integer answer