Question

# In general, tan (α + β) is not equal to tan α + tan β. However, there are some values of α and β for which they are equal. Find such α and β, and do t

Right triangles and trigonometry

In general, $$\tan(\alpha+\beta)$$ is not equal to $$\tan\alpha+\tan\beta$$. However, there are some values of $$\alpha$$ and $$\beta$$ for which they are equal. Find such $$\alpha$$ and $$\beta$$ and do the same for $$\tan(\alpha-\beta)$$

2021-06-07

Let $$\displaystyleβ={0}°$$ so that:

$$\tan(\alpha+0^{\circ})=\tan\alpha+\tan0^{\circ}$$

$$\tan\alpha=\tan\alpha$$

Hence,

$$\tan(\alpha+\beta)=\tan\alpha+\tan\beta$$

for any value of $$\alpha\alpha$$ given that $$\beta=0^{\circ}$$

$$\alpha=30^{\circ}$$ and $$\beta=0^{\circ}$$

Do the same for $$\tan(\alpha−\beta)$$. Let $$\beta=0^{\circ}$$ so that:

$$\tan(\alpha−0^{\circ})=\tan\alpha−\tan0^{\circ}$$

$$\tan\alpha=\tan\alpha$$

Hence, $$\tan(\alpha-\beta)=\tan\alpha-\tan\beta$$ for any value of αα given that $$\beta=0^{\circ}$$. A possible answer is when:

$$\alpha=45^{\circ}$$ and $$\beta=0^{\circ}$$

2021-08-11

EXplained on video