Use app×
Ask a Question
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

If `A, B, C, D` be the angles of acyclic quadrilateral, show that : `cosA +cosB+cosC+cosD=0`.

← Prev Question Next Question →
0 votes
96 views
in Trigonometry by (94.1k points)
closed by
If `A, B, C, D` be the angles of acyclic quadrilateral, show that : `cosA +cosB+cosC+cosD=0`.
Play Quiz Games with your School Friends. Click Here

1 Answer

0 votes
by (91.2k points)
selected by
 
Best answer
We know that the opposite angles of a cyclic quadrilateral are supplementary, i.e., `A+C=pi" and " B+ D=pi`. Therefore,
`A=pi-C" and " B=pi-D`
`rArr cosA=cos(pi-C)=-cosD`
and `cosB=cos(pi-D)=-cosD`
`:. cosA+cosB+cosC+cos D`
`=-cosC-cosD+cosC+cosD=0`
← Prev Question Next Question →

Find MCQs & Mock Test

  1. JEE Main 2025 Test Series
  2. NEET Test Series
  3. Class 12 Chapterwise MCQ Test
  4. Class 11 Chapterwise Practice Test
  5. Class 10 Chapterwise MCQ Test
  6. Class 9 Chapterwise MCQ Test
  7. Class 8 Chapterwise MCQ Test
  8. Class 7 Chapterwise MCQ Test

Related questions

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

User Contribution to Sarthaks eConnect
Managed by Sarthaks Digitizing India
...