Question

10. Find the value of
tan 60°-tan 30°
1+tan 60° tan 30°​

Answer 1

Answer:

tan60°-tan30°=2/√3

1+tan60°+tan30°=4

Answer 2

Answer:

(a) tan 60°-tan 30°=  $\frac{2\sqrt{3} }{3}$

(b) 1+tan 60° tan 30° = 2

Explanation:

• tan 60° = √3
• tan 30°= $\frac{1}{\sqrt{3} }$

(a) tan 60°-tan 30°

Substituting the values, we get:

=  $\sqrt{3} - \frac{1}{\sqrt{3} }$

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

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

= $\frac{2}{\sqrt{3} }$

= $\frac{2}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3}}$                                                     (Rationalizing)

= $\frac{2\sqrt{3} }{3}$

Hence, tan 60°-tan 30° = $\frac{2\sqrt{3} }{3}$

(b) 1+tan 60° tan 30°

Substituting the values, we get:

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

= 1 + 1

= 2

Hence, 1+tan 60° tan 30° = 2

Hope you got that.

Thank You.