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
7.6k views
in Trigonometry by (36.2k points)
closed by

Prove that:

\(\frac{1+cos(A-B)\,cos\,C}{1+cos(A-C)\,cos\,B}=\frac{a^2+b^2}{a^2+c^2}.\)

1 Answer

+1 vote
by (33.4k points)
selected by
 
Best answer

LHS = \(\frac{1+cos(A-B)\,cos\,C}{1+cos(A-C)\,cos\,B}\)

\(=\frac{1-cos(A-B)\,cos\,(A+B)}{1-cos(A-C)\,cos\,(A+C)}\)

\(=\frac{1-(cos^2\,A-sin^2\,B)}{1-(cos^2A-sin^2\,C)}\)

\(=\frac{sin^2\,B+1-cos^2\,A}{sin^2\,C+1-cos^2\,A}\) 

\(\frac{a^2+b^2}{a^2+c^2}\) = RHS

∴ LHS = RHS

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

...