Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.6k views
in Trigonometry by (46.1k points)
closed by

Without using trigonometric tables, prove that: tan 1° . tan 2° . tan 3° . .... tan 89° = 1

1 Answer

+1 vote
by (49.2k points)
selected by
 
Best answer

Given exp. 

= tan (90° – 89°) tan (90° – 88°) tan (90° – 87°) ... tan 87° . tan 88° . tan 89° 

= cot 89°.cot 88° . cot 87° ..... tan 87° . tan 88° . tan 89° 

= (cot 89°.tan 89°) (cot 88°.tan 88°) .... (cot 44°.tan 44°).tan45° 

= 1 × 1 × ...... × 1 × 1 = 1           (∵ tan 45° = 1, cot θ. tan θ = 1)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...