Question

if a + b + c is equal to 270 degree then find the value of cos 2A + cos 2 b + cos2c

Answer 1

A+B+C=270

A+B=270-C

C=270-(A+B)

cos2A+cos2B+cos2C

= 2 cos(2A+2B/2)cos(2A-2B/2)+cos2C

=2cos(A+B)cos(A-B)+ cos2C

=2cos(270-C) cos(A-B)+ cos2C

=-2sinC cos(A-B)+ cos2C

= - 2sinC cos(A-B)+1-2sin²C

=1-2sinC [ cos ( A- B) + sinC ]

=1-2 SinC [ cos( A-B) + sin( 270-(A+B) ]

=1- 2 SinC [ cos( A-B) - cos( A+ B) ]

= 1 -2 sinC [2 sinAsinB]

=1-4 SinAsinBsinC