Q. 50

If 1+sin2θ = 3 sinθ . cosθ, then prove that tan θ = 1 or 1/2.

Given: 1+sin2θ =3 sin θ cos θ

Divide by cos2 θ to both the sides, we get

sec2 θ + tan2 θ = 3 tan θ

1+ tan2 θ+ tan2 θ = 3tan θ

2 tan2 θ –3tan θ +1 = 0

Let tanθ = x

2x2 – 3x +1 = 0

2x2 – 2x – x +1 = 0

2x ( x 1) 1(x 1) = 0

(2x 1)(x 1) = 0

Putting each of the factor = 0, we get

x = 1 or

And above, we let tan θ = x

Hence Proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trigonometric Identities33 mins
Champ Quiz | Trigonometric Identities33 mins
NCERT | Trigonometric Identities52 mins
Quiz | Task on Trigonometric Ratios46 mins
Trigonometric Identities44 mins
Solving NCERT Questions on Trigonometric Identities56 mins
Algebraic Identities48 mins
Quiz | Practice Important Questions on Trigonometrical Identities46 mins
Quiz on Trigonometric Ratios31 mins
T- Ratios of Specified Angles58 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses