Question 31

Find $$\tan 75^\circ$$, by splitting $$75^\circ as (45^\circ + 30^\circ)$$.

Solution

Tan(A + B )= $$\frac {tan A + tan B}{1- tan A\tan B}$$

$$\tan 75^\circ$$, by splitting $$75^\circ as (45^\circ + 30^\circ)$$.

$$\tan 45^\circ$$ =1

$$\tan 30^\circ$$ =$$\tan\frac{1}{\sqrt{3}}$$

Tan(45 + 30 )= $$\frac {tan 45 + tan 30}{1- tan 45\times \tan 30}$$

Tan(A + B )= $$\frac {1 +\frac{1}{\sqrt{3}}}{1- \frac{1}{\sqrt{3}}}$$

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