Question

If 1+sin^2θ=3 sinθcosθ. Find the value of tanϑ

Answer 1

Answer: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

Step-by-step explanation: