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
90 views
in Mathematics by (92.3k points)
closed by
सिद्ध कीजिए कि -
`tan^(-1)1+tan^(-1)2+tan^(-1)3=pi`

1 Answer

0 votes
by (93.6k points)
selected by
 
Best answer
`LH.S.=tan^(-1)+tan^(-1)2+tan^(-1)3`
`=(pi)/(4)+((pi)/(2)-cot^(-1)2)+((pi)/(2)-cot^(-1)3),`
`[because tan^(-1)x=(pi)/(2)-cot^(-1)x" सभी "x in R " के लिए "]`
`=(pi)/(4)+pi-(cot^(-1)2+cot^(-1)3)`
`=(pi)/(4)+pi-[tan^(-1)((1)/(2))+tan^(-1)((1)/(3))]`
`" "[because cot^(-1)x=tan^(-1)((1)/(x))]`
`=(pi)/(4)+pi-tan^(-1)(((1)/(2)+(1)/(3))/(1-(1)/(2)xx(1)/(3)))`
`=(pi)/(4)+pi-tan^(-1)(((5)/(6))/((5)/(6)))`
`=(pi)/(4)+pi-tan^(-1)(1)`
`=(pi)/(4)+pi-(pi)/(4)`
`=pi=R.H.S." "` यही सिद्ध करना था ।

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

...