If 0°<A,B<90° , cosA=45 and sinB=35 , then the value of cos(A+B) is

cosA=45 ,sinB=35 sinA=35 ,cosB=45 cos(A+B)=cosAcosB−sinAsinB =45.45−35.35 =1625−925=725

If 0°<A,B<90° , cosA=45 and sinB=35 , then the value of cos(A+B) is

cosA=45 ,sinB=35 sinA=35 ,cosB=45 cos(A+B)=cosAcosB−sinAsinB =45.45−35.35 =1625−925=725

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If $0 ° < A, B < 90 °$ , $\cos A = \frac{4}{5}$ and $\sin B = \frac{3}{5}$ , then the value of $\cos (A + B)$ is

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\frac{25}{7}

5

\frac{7}{25}

4

answer is C.

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Detailed Solution

\cos A = \frac{4}{5}

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

$\sin A = \frac{3}{5}$ , $\cos B = \frac{4}{5}$

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

$= \frac{4}{5} . \frac{4}{5} - \frac{3}{5} . \frac{3}{5}$

$= \frac{16}{25} - \frac{9}{25} = \frac{7}{25}$

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If 0°<A,B<90° , cosA=45 and sinB=35 , then the value of cos(A+B) is

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If $0 ° < A, B < 90 °$ , $\cos A = \frac{4}{5}$ and $\sin B = \frac{3}{5}$ , then the value of $\cos (A + B)$ is