Question

For positive acute angles A and B, it is known that tan A = 21/20 and cos B = 15/17

Find the value of sin(A + B) in simplest form.

Answer 1

Given:-

`\tan A=(21)/(20),\cos B=(15)/(17)`

To find:-

`\sin (A+B)`

The formula is,

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

Now we substitute the values. we get,

`\sin (A+B)=21*(15)/(17)+20\sqrt[]{(1-\frac{15^2}{17^{^2^{}}})}`

Now we get,

`\begin{gathered} \sin (A+B)=21*(15)/(17)+20\sqrt[]{(1-\frac{15^2}{17^{^2^{}}})} \\ \sin (A+B)=(315)/(17)+(20)/(17)\sqrt[]{17^2-15^2} \\ \sin (A+B)=(315)/(17)+(20)/(17)*8 \\ \sin (A+B)=(315)/(17)+(160)/(17) \\ \sin (A+B)=(475)/(17) \end{gathered}`

So the required value is,

`(475)/(17)`