Question

Without using trigonometric tables, prove that:
2Cos 67/Sin23 - tan40/Cot50 - Cos0 + tan15 tan25 tan60° tan65 tan75°+ 3(Sin36/Cos54°)² -2(Tan18°/Cos72°)³ + 2 tan13° tan21° tan69° tan77° = ✓3+3.


I am challenging a genius to solve this question.only genius can solve this question.please please solve this.

Answer 1

Hiii friend,

2 Cos 67° / Sin23° - Tan40°/Cot50° - Cos0° + Tan15° × Tan25° × Tan60° × Tan65° × Tan75° + 3(Sin36° / Cos 54°)² - 2( Tan18° / Cos72°)³ + 2 × Tan13° × Tan21° × Tan69° × Tan77° = ✓3+3

We have,


LHS = 2 Cos67° / Sin23° - Tan40°/Cot50° - Cos0° + Tan15° × Tan25° × Tan60° × Tan65° × Tan75° × 3(Sin36°/Cos54°)² - 2(Tan18°/Cos72°)³ + 2 Tan13° × Tan21° × Tan69° × Tan77°


=> 2Cos67°/Sin(90-67°) - Tan40°/Cot(90-40°) -1 + Tan15° × Tan25° × ✓3 × Tan(90-25°) × Tan(90°-15°) + 3 × (Sin36°/Cos(90-36)}² - 2 × {Tan18°/Cot(90°-18°)²}³ + 2 × Tan13° × Tan21° × Tan(90-21) × Tan (90-13)

=> 2 × Cos67°/Cos67° - Tan40°/Tan40° - 1 + Tan15° × Tan25° × ✓3 × Cot25° × cot15° + 3 × Sin36/Sin36°)² -2 × (Tan18°/Tan18°)³ + 2 × Tam13° × Tan21° × Cot21° × Cot13°



=> 2 × (1) -1 -1 +✓3 + 3 × (1)² - 2 × (1)³ +2 = 2-2+✓3+3-2+2 = ✓3+3 = RHS.


Hence,


LHS = RHS = ✓3+3.



HOPE IT WILL HELP YOU...... :-)

Answer 2

I hope this will help you


-by ABHAY