Question

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

Answer 1

`\boxed{ \boxed{ \cos {}^(2) ( \theta) = (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 (3)/(4) + \cos {}^(2) ( \theta) = 1`

`\longrightarrow \cos{}^(2)( \theta) = 1 - (3)/(4)`

`\longrightarrow \cos {}^(2) ( \theta) = (4 - 3)/(4)`

`\longrightarrow \cos {}^(2) ( \theta) = (1)/(4)`

`\large\mathfrak{{\pmb{\underline{\orange{hope \: \: it \: \: helps \: \: you.....}}{\orange{}}}}}`