Question

Evaluate without using trignometric tables
Tan12°Tan38°Tan52°Tan60°Tan78°
Plz give answer step by step

Answer 1

Answer:

tan(90-78)tan(90-52)tan52°×√3tan78°

cot78°cot52°tan52° tan78°×√3

=√3. (cot×tan=1)

Answer 2

$\tan 12\tan 38\tan 52\tan 60\tan 78=\sqrt{3}$

Step-by-step explanation:

We have,

$\tan 12.\tan 38.\tan 52.\tan 60.\tan 78$

To find, the value of $\tan 12\tan 38\tan 52\tan 60\tan 78=?$

∴ $\tan 12.\tan 38.\tan 52.\tan 60.\tan 78$

$=\tan 12.\tan 38.\tan (90-38).\tan 60.\tan (90-12)$

Using trigonometric formula,

$\tan (90-A)=\cot A$

$=\tan 12. \tan 38. \cot 38. \tan 60. \cot 12$

$=(\tan 12.\cot 12).(\tan 38 \cot 38)\tan 60$

Using trigonometric formula,

$\tan A.\cot A=1$

$=(1).(1)\tan 60$

$=\tan 60$

= $\sqrt{3}$

Hence, $\tan 12\tan 38\tan 52\tan 60\tan 78=\sqrt{3}$