Question

If 1+ sin 2 theta =3sin theta cos theta then prove that tan theta = 1 or 1/2 ?

Answer 1

Solution – 
 
1 + sin^2θ = 3 sinθ cosθ 
 
Divide both side of the equation with cos^2θ 
 
1/cos^2θ + sin^2θ/cos^2θ = 3 sinθ/cosθ 
 
sec^2θ + tan^2θ = 3tanθ 
 
1 + tan^2θ + tan^2θ = 3tanθ 
 
1 + 2tan^2θ – 3tanθ = 0 
 
Substitute tanθ = a 
 
2a^2 – 3a + 1 = 0 
 
Solve the quadratic equation to find out the roots. 
 
2a^2 – 2a – a + 1 = 0 
 
2a (a – 1) – 1 (a – 1) = 0 
 
(2a – 1) ( a – 1) = 0 
 
2a – 1 = 0 and (a – 1) = 0 
 
2a = 1 and a = 1 a = 1/2 and a = 1 
 
Hence a = tanθ 
 
tanθ = 1/2 and tanθ = 1

Answer 2

Answer:tan theta=1 ,tan theta = 1/2

Step-by-step explanation:

sin square theta + cos square theta +sin square theta = 0

2sin square theta - 3 sin theta cos theta + cos square theta = 0

2 sin square theta - 2 sin theta cos theta - sin theta cos theta + cos square theta = 0

(sin theta - cos theta)(2 sin theta - cos theta ) = 0

sin theta - cos theta = 0 or 2 sin theta - cos theta = 0

sin theta = cos theta or 2 sin theta = cos theta

sin theta /cos theta = 1 or sin theta/cos theta = 1/2

tan theta =1 & tan theta = 1/2