What is 1+sin²(cos^{-1}({3}{{17}})) equal to ?

Correct Answer is : 251725/171725

Correct Answer is : 251725/171725

Test Index

UPSC NDA II 2023 Mathematics Solved Paper

Question : 28 of 120

Marks: +1, -0

What is

1+sin^{2}(cos^{-1}(\frac{3}{\sqrt{17}}))

equal to ?

Solution:

Concept:

Use the inverse cosine to express

\cos \theta

as a ratio, then compute

\sin^2 \theta

using Pythagoras theorem.

Explanation:

Let

\theta = \cos^{-1}\left(\frac{3}{\sqrt{17}}\right)

Then

\cos \theta = \frac{3}{\sqrt{17}} = \frac{\text{base}}{\text{hypotenuse}}

Using Pythagoras:

\text{perpendicular}^2 = \text{hypotenuse}^2 - \text{base}^2 = 17 - 9 = 8

\text{perpendicular} = 2\sqrt{2}

Thus

\sin \theta = \frac{\text{perpendicular}}{\text{hypotenuse}} = \frac{2\sqrt{2}}{\sqrt{17}}

, and

\sin^2 \theta = \frac{8}{17}

Now

1 + \sin^2 \theta = 1 + \frac{8}{17} = \frac{25}{17}

Answer:

\frac{25}{17}

, which corresponds to option A.

Go to Question:

Prev Question

Next Question