Q53 of 76 Page 52

Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is

We have, tan x + sec x = 2 cos x



⇒ 1+sin x = 2cos2x


⇒ 2cos2x-sin x-1 = 0


⇒ 2(1-sin2x)-sin x-1 = 0


⇒ 2-2sin2x-sin x-1 = 0


⇒ 2sin2x+sin x-1 = 0


Since, the equation is a quadratic equation in sin x, it will have 2 solutions.

More from this chapter

All 76 →
51

If then the value of (1+ tanα) (1 + tanβ) is

 52

If and θ lies in third quadrant then the value of is

 54

The value of is given by

 55

If A lies in the second quadrant and 3 tan A + 4 = 0, then the value of 2 cot A– 5 cos A + sinA is equal to