Maths / Introduction to Trigonometry / Trigonometric ratios of Complementary Angles

QUESTION
 

large tan 1^0. tan 2^0. tan 3^0. ......... tan 89^0 = _____________________

OPTIONS
A. 

1

B. 

large tan90

C. 

large tan45

D. 

0

Right Option : C

EXPLANATION
Explain TypeExplanation Content
Text

tan 1° tan 2° tan 3° ...... tan 89°

= tan 1° tan 2° ...... tan 44° tan 45° tan 46° ...... tan 88° tan 89°

= (tan 1° ∙ tan 89°) (tan 2° ∙ tan 88°) ...... (tan 44° ∙ tan 46°) ∙ tan 45°

= {tan 1° ∙ tan (90° - 1°)} ∙ {tan 2° ∙ (tan 90° - 2°)} ...... {tan 44° ∙ tan (90° - 44°)} ∙ tan 45°

= (tan 1° ∙ cot 1°)(tan 2° ∙ cot 2°) ...... (tan 44° ∙ cot 44°) ∙ tan 45°, [Since tan (90° - θ) = cot θ]

= (1)(1) ...... (1) ∙ 1, [since tan θ ∙ cot θ = 1 and tan 45° = 1]

= 1

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