Question

Number of solutions of the equation tanx – secx = 2cosx lying in the interval [0, 2π] is​

Answer 1

So, there can be three solutions: 30°, 150° and 270°.

The number of solution of tan x + sec x = 2 cos x in [0, 2π) is

A. 0

B. 1

C. 2

D. 3

Answer

Answertan x + sec x = 2 cos x

Answertan x + sec x = 2 cos xMultiply equation by cos x

Answertan x + sec x = 2 cos xMultiply equation by cos x1 + sin x = 2 cos2 x

Answertan x + sec x = 2 cos xMultiply equation by cos x1 + sin x = 2 cos2 x1 + sin x = 2(1 - sin2 x)

Answertan x + sec x = 2 cos xMultiply equation by cos x1 + sin x = 2 cos2 x1 + sin x = 2(1 - sin2 x)2 sin2 x + sin x - 1 = 0

Answertan x + sec x = 2 cos xMultiply equation by cos x1 + sin x = 2 cos2 x1 + sin x = 2(1 - sin2 x)2 sin2 x + sin x - 1 = 0(2 sin x - 1)(1 + sin x) = 0

Answertan x + sec x = 2 cos xMultiply equation by cos x1 + sin x = 2 cos2 x1 + sin x = 2(1 - sin2 x)2 sin2 x + sin x - 1 = 0(2 sin x - 1)(1 + sin x) = 0sin x = 1/2 ; sin x = -1

Answertan x + sec x = 2 cos xMultiply equation by cos x1 + sin x = 2 cos2 x1 + sin x = 2(1 - sin2 x)2 sin2 x + sin x - 1 = 0(2 sin x - 1)(1 + sin x) = 0sin x = 1/2 ; sin x = -1So, there can be three solutions: 30°, 150° and 270°.

Answertan x + sec x = 2 cos xMultiply equation by cos x1 + sin x = 2 cos2 x1 + sin x = 2(1 - sin2 x)2 sin2 x + sin x - 1 = 0(2 sin x - 1)(1 + sin x) = 0sin x = 1/2 ; sin x = -1So, there can be three solutions: 30°, 150° and 270°.The correct option is D.