Maths / Introduction to Trigonometry / Trigonometric ratios of Complementary Angles

QUESTION

$\dpi{120} \fn_jvn \large tan 1^0. tan 2^0. tan 3^0. ......... tan 89^0$ = _____________________

 OPTIONS A. 1 B. $\dpi{120} \fn_jvn \large tan90$ C. $\dpi{120} \fn_jvn \large tan45$ 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

View Contents
(Concept based Learning and Testing for [6th - 10th], NTSE, Bank & Govt. Exams)
Self Learning
Testimonials
Student Feedback on Methodology - Khushal Bindal C/o ABHYAS Academy
6th
The methodology of Abhyas academy is nice. The teachers over here explain us the chapter so nicely and accurately so that we can tell the whole chapter in class before the teacher in the class tell up. They always build us to be the topper.

#### Other Testimonials

Courses We Offer
(Concept based Learning and Testing for [6th - 10th], NTSE, Bank & Govt. Exams)