Question

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$1 - {cos}^{2} θ = \frac{1}{4} \: then \: θ \: =$
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Answer 1

Answer:

$1 - {cos}^{2} θ = \frac{1}{4}$

$from \: the \: fromula \\ { \sin}^{2} θ \: + { \cos }^{2} θ = 1$

$1 - { \cos}^{2} θ = { \sin}^{2} θ$

$then \: \\ { \sin }^{2} θ = \frac{1}{4}$

$\sin θ = \frac{1}{2}$

$θ = \frac{1}{2} \sin ^{ - 1}$

$θ = 30$

Answer 2

1−cos 2 θ= 41

$→\begin{gathered}from \: the \: fromula \\ { \sin}^{2} θ \: + { \cos }^{2} θ = 1\end{gathered}$

FROM THE FORMULA $⟹ 2 θ+cos θ=11-{ \cos}^{2} θ = { \sin}^{2} θ1−cos2 θ=sin2θ$

$→\begin{gathered}then \: \\ { \sin }^{2} θ=\frac{1}{4} \end{gathered}$

then

sin 2 θ= 41 $\sin θ = \frac{1}{2}sinθ= 21$

$θ = \frac{1}{2} \sin ^{ - 1}θ=21 sin −1$

θ = 30θ=30