Give that tan o =3/4 Fine a sim b cos c7tan + 5 cos

We can use a right-angled triangle where $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$.
Let the opposite side be $3k$ and the adjacent side be $4k$ for some constant $k$.
Using the Pythagorean theorem, the hypotenuse $h$ is:

$$h = \sqrt{(3k)^2 + (4k)^2} = \sqrt{9k^2 + 16k^2} = \sqrt{25k^2} = 5k$$

Now we can find $\sin \theta$ and $\cos \theta$:

$$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3k}{5k} = \frac{3}{5}$$ $$\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{4k}{5k} = \frac{4}{5}$$

Substitute the given value of $\tan \theta$ and the calculated value of $\cos \theta$:

$$7 \tan \theta + 5 \cos \theta = 7 \left(\frac{3}{4}\right) + 5 \left(\frac{4}{5}\right)$$ $$= \frac{21}{4} + \frac{20}{5}$$ $$= \frac{21}{4} + 4$$

To add these fractions, find a common denominator:

$$= \frac{21}{4} + \frac{4 \times 4}{4}$$ $$= \frac{21}{4} + \frac{16}{4}$$ $$= \frac{21 + 16}{4}$$ $$= \frac{37}{4}$$

The value of the expression is $\frac{37}{4}$.