Question

द्ध कीजिए (Prove that)-
cos A cos (C - A) - sin A sin (C - A) = cos C​

Answer 1

Answer:

we have

sinA+sinB=−sinC

and

cosA+cosB=−cosC

squaring and adding both we get

2+2cos(A−B)=1

that is

cos(A−B)=−12

⟹

A−B=2π3

similarly

B−C=−4π3

and

C−A=2π3

Now

cos3A=cos(3(B+2π3))=cos(3B+2π)=cos3B

similarly

cos3C=cos3B

Hence

cos3A+cos3B+cos3C=3cos3A=3cos(A+A+A)=3cos(A+B+2π3+C−2π3)=3cos(A+B+C)