Question

Find the exact value of cos2theta if sin2theta=3/4 and theta is between 0 and 90 degree

Answer 1

Answer :

$\boxed{ \boxed{ \cos {}^{2} ( \theta) = \dfrac{1}{4} }}$

Solution :

According to a Trigonometric Identity :

$\hookrightarrow \mathrm{\sin {}^{2} ( \theta) + \cos {}^{2} ( \theta) = 1}$

Now, let's solve for $\cos²(\theta)$

$\longrightarrow \dfrac{3}{4} + \cos {}^{2} ( \theta) = 1$

$\longrightarrow \cos{}^{2}( \theta) = 1 - \dfrac{3}{4}$

$\longrightarrow \cos {}^{2} ( \theta) = \dfrac{4 - 3}{4}$

$\longrightarrow \cos {}^{2} ( \theta) = \dfrac{1}{4}$

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