If 4 cos2 θ – 3 = 0, then sin θ =………A) 1/2B) -1/2C) 1/√2D

1.	If 4 cos2 θ – 3 = 0, then sin θ =………A) 1/2B) -1/2C) 1/√2D) √3/2
Answer» Correct option is: A) \(\frac{1}{2}\) Given that \(4\, cos^2\theta -3 = 0\) \(\therefore\) \(cos^2\theta = \frac 34\) \(1- sin^2\theta = \frac 34\) (\(\because\) \(cos^2\theta = 1-sin^2\theta)\) \(Sin^2\theta = 1 - \frac 34 = \frac 14\) sin \(\theta\) = \(\pm \frac 12\) sin \(\theta\) = \(\frac 12\) or sin \(\theta\) = \(\frac {-1}2\) Correct option is: A) \(\frac{1}{2}\)

If 4 cos2 θ – 3 = 0, then sin θ =………A) 1/2B) -1/2C) 1/√2D) √3/2

Answer»

Correct option is: A) \(\frac{1}{2}\)

Given that \(4\, cos^2\theta -3 = 0\)

\(\therefore\) \(cos^2\theta = \frac 34\)

\(1- sin^2\theta = \frac 34\) (\(\because\) \(cos^2\theta = 1-sin^2\theta)\)

\(Sin^2\theta = 1 - \frac 34 = \frac 14\)

sin \(\theta\) = \(\pm \frac 12\)

sin \(\theta\) = \(\frac 12\) or sin \(\theta\) = \(\frac {-1}2\)

Correct option is: A) \(\frac{1}{2}\)