Question

sin^2 theta -2 cos theta+1/4 =0 find value(°) of theta

Answer 1

hence
theta = 60°
understand the related identities used

Answer 2

Answer:

60°

Step-by-step explanation:

Given : $sin^2 \theta -2 cos \theta+\frac{1}{4} =0$

To Find : $\theta$

Solution :

$sin^2 \theta -2 cos \theta+\frac{1}{4} =0$

Using identity : $sin^2x +Cos ^2 x= 1$

$1-cos^2\theta -2 cos \theta+\frac{1}{4} =0$

$-cos^2\theta -2 cos \theta+\frac{5}{4} =0$

$cos^2\theta +2 cos \theta-\frac{5}{4} =0$

Substitute x in place of $cos \theta$

$x^2+2 x-\frac{5}{4} =0$

$x= \frac{-5}{2}, \frac{1}{2}$

Since range of cos is -1 to 1

So, Reject -5/2

So, $Cos \theta = \frac{1}{2}\\\theta = Cos^{-1}(\frac{1}{2})\\\theta = Cos^{-1}(cos 60^{\circ})\\\theta = 60^{\circ}$

Hence The value of theta is 60°