1.

\( \cos 2 A-\cos 2 B+\cos 2 C=1-4 \sin A \cos B \sin C \)uhyygyuuuhhu

Answer»

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.



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