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 the same for tan (α - β).

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Let β=0° so that: tan⁡(α+0°)=tan⁡α+tan⁡0°  tan⁡α=tan⁡α  Hence, tan⁡(α+β)=tan⁡α+tan⁡β for any value of αα given that β=0°. A possible answer is when:  α=30° and β=0°  Do the same for tan⁡(α−β).Let β=0° so that:  tan⁡(α−0°)=tan⁡α−tan⁡0°  tan⁡α=tan⁡α  Hence, tan⁡(α−β)=tan⁡α−tan⁡β for any value of αα given that β=0°. A possible answer is when:  α=45° and β=0°

In general, tan (α + β) is not equal to

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