Question

If 4 tan 0= sin2 0 +sin2 (90° 0) 4sin0-cos0+1/4sin2(90°-0)

Answer 1

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

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