≤ft[ ^{-1}≤ft(3/5)+ ^{-1}≤ft(12/13)]=

Correct Answer is : 336533/656533

Correct Answer is : 336533/656533

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MHTCET 11 May 2024 Shift 1 Paper

Question : 147 of 150

Marks: +1, -0

\cos \left[\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)\right]=

Solution:

Concept:

Use the identity

\cos(A+B) = \cos A \cos B - \sin A \sin B

and simplify inverse trigonometric values.

Explanation:

Let

A = \sin^{-1}\left(\frac{3}{5}\right)

and

B = \cos^{-1}\left(\frac{12}{13}\right)

Then

\cos(A+B) = \cos A \cos B - \sin A \sin B

We have

\sin A = \frac{3}{5}

, so

\cos A = \sqrt{1 - \left(\frac{3}{5}\right)^2} = \frac{4}{5}

We have

\cos B = \frac{12}{13}

, so

\sin B = \sqrt{1 - \left(\frac{12}{13}\right)^2} = \frac{5}{13}

Substitute these values into the identity:

\cos(A+B) = \frac{4}{5} \times \frac{12}{13} - \frac{3}{5} \times \frac{5}{13}

= \frac{48}{65} - \frac{15}{65} = \frac{33}{65}

Answer:

\frac{33}{65}

, which is option C.

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