Question

The value of $sin^2(cos^{-1}(\frac{3}5))$ is equal to

• A. $\frac{4}{5}$
• B. $\frac{16}{25}$
• C. $\frac{9}{25}$
• D. $\frac{5}{3}$
• E. $\frac{25}{9}$

Answer 1

The Correct Option is B

Given:

\(\sin^2 (\cos^{-1} (\frac{3}{5}))\) 

Let \(\theta = \cos^{-1} (\frac{3}{5})\), so we have:

\(\cos \theta = \frac{3}{5}\)

Using the Pythagorean identity:

\(\sin^2 \theta + \cos^2 \theta = 1\)

Substituting \(\cos \theta = \frac{3}{5}\):

\(\sin^2 \theta + \left(\frac{3}{5}\right)^2 = 1\)

\(\sin^2 \theta + \frac{9}{25} = 1\)

\(\sin^2 \theta = 1 - \frac{9}{25}\)

\(\sin^2 \theta = \frac{25}{25} - \frac{9}{25}\)

\(\sin^2 \theta = \frac{16}{25}\)

Thus, the correct answer is:

\(\frac{16}{25}\)