Question

Find tan(a-b) sin a=4/5 tan b=3/4 Give the exact answer, not a decimal approximation.

Answer 1

Answer: 0.2916666665

Step-by-step explanation:

Answer 2

Answer:

$\frac{7}{24}$

Step-by-step explanation:

By the Pythagorean Theorem, we know

$\cos^2a=1-\sin^2a$.

With this, we can find $\cos a$ by plugging in what we know for $\sin a$:

$\cos^2a=1-(\frac{4}{5})^2\\~~~~~~~~=1-\frac{16}{25}\\~~~~~~~~=\frac{9}{25}$.

Taking the square root, we get

$\cos a=\frac{3}{5}$ .

Note: there seems to be a problem with the question? It doesn't specify what range $a$ lies in, so we don't know whether $\cos a$ is positive or negative. In this case, I assumed it was positive.

From this, we can find $\tan a$:

$\tan a=\frac{\sin a}{\cos a}\\~~~~~~~=\dfrac{\frac{4}{5}}{\frac{3}{5}},$

so $\tan a=\frac{4}{3}$.

Using the $\tan$ difference formula, we know

$\tan (a-b)=\dfrac{\tan a -\tan b}{1+\tan a\tan b}$ .

Plugging in the values we know for $\tan a$ and $\tan b$, we get

$\tan(a-b)=\dfrac{\frac{4}{3}-\frac{3}{4}}{1+\frac{4}{3}\cdot\frac{3}{4}}\\~~~~~~~~~~~~~~=\dfrac{\frac{7}{12}}{1+1}\\~~~~~~~~~~~~~~=\boxed{\frac{7}{24}}~.$