Question

without usng trigonometric table, prove that : tan 7 tan 23 tan 60 tan 67 tan 83 = root 3

Answer 1

hey mate
here's the solution

Answer 2

Here your answer goes

Correction as below :-

tan 7° tan 23° tan 60° tan 67° tan 83° =  $\sqrt{3}$

Step :- 1

Grouping Term in such a way that the angle involved are complementary i.e. there sum is 90°, We have

Given ,

tan 7° tan 23° tan 60° tan 67° tan 83° =  $\sqrt{3}$

⇒ ( tan 23° tan 67° ) ( tan 7° tan 83° ) tan 60°

Step :- 2

∴ tan 67° = tan ( 90° - 23° ) = Cot 23°

∴ tan 83° = tan ( 90° - 7° ) = Cot 7°

⇒ ( tan 23° Cot 23° ) ( tan 7° Cot 7° ) tan 60°

⇒ 1 *1 * $\sqrt{3}$ = $\sqrt{3}$

⇒ $\sqrt{3} = \sqrt{3}$

Hence , Proved

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