If A + B + C = π , prive that COS 2A - COS 2B + COS 2C =1 - 4SIN A COS B SIN C
\( \cos 2 A-\cos 2 B+\cos 2 C=1-4 \sin A \cos B \sin C \)uhyygyuuuhhu
5 views
1 Answers
Here we want +1 and as such we write cos2A=1−2sin2 A and combine the other two terms.
L.H.S. =1−2sin2A+2sin(B+C)sin(C−B) (Note)
=1−2sin2A−2sinAsin(B−C) [∵sin(−θ)=−sinθ]
=1−2sinA[sinA+sin(B−C)]
=1−2sinA[sin(B+C)+sin(B−C)]
=1−2sinA(2sinBcosC)
=1−4sinAsinBcosC.
5 views
Answered