Question

3. Find the value of
tan 75°– tan 30°, tan 75º tan 30°.​

Answer 1

Answer:

$\frac{4}{\sqrt{3}(\sqrt{3}-1}$,$\frac{\sqrt{3}+1}{3-\sqrt{3}}$

Step-by-step explanation:

  tan75°

= tan(45°+30°)

= $\frac{tan30+tan45}{1-tan30.tan45}$

= $\frac{\frac{1}{\sqrt{3}}+1 }{1-\frac{1}{\sqrt{3} } }$

= $\frac{\sqrt{3}+1 }{\sqrt{3}-1}$

tan75° - tan30°

= $\frac{\sqrt{3}+1 }{\sqrt{3}-1} - \frac{1}{\sqrt{3} }$

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

=$\frac{4}{\sqrt{3}(\sqrt{3}-1)}$

Similarly do other