In a - ABC- cos A-3-5 and cos B-5-13- The value of cos C can be

The correct option is B 33/65 We know, cos(A+B) #160; = cos C =cos A.cos B sin A.sin B ∴cos C= (cos Acos B sin Asin B) = (156 ...

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Standard XII

Mathematics

Cos(A+B)Cos(A-B)

In a Δ ABC,...

Question

In a $Δ A B C, cos A = \frac{3}{5}$ and $cos B = \frac{5}{13} .$ The value of $cos C$ can be

\frac{7}{13}

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\frac{12}{13}

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\frac{33}{65}

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none of these

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Solution

The correct option is B $\frac{33}{65}$
We know, $cos (A + B)$ $= - cos C$
$= cos A . cos B - sin A . sin B$
$∴ cos C = - (cos A cos B - sin A sin B)$
$= - (\frac{15}{65} - \frac{4.12}{65})$
$= - (\frac{15 - 48}{65})$
$= \frac{33}{65}$

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In a ΔABC,cosA=35 and cosB=513. The value of cosC can be

The correct option is B 3365We know, cos(A+B) =−cosC=cosA.cosB−sinA.sinB∴cosC=−(cosAcosB−sinAsinB)=−(1565−4.1265)=−(15−4865)=3365

In a $Δ A B C, cos A = \frac{3}{5}$ and $cos B = \frac{5}{13} .$ The value of $cos C$ can be

The correct option is B $\frac{33}{65}$
We know, $cos (A + B)$ $= - cos C$
$= cos A . cos B - sin A . sin B$
$∴ cos C = - (cos A cos B - sin A sin B)$
$= - (\frac{15}{65} - \frac{4.12}{65})$
$= - (\frac{15 - 48}{65})$
$= \frac{33}{65}$