Question

3. If a = cis 2c, b = cis 2B, c = cis 2y and d = cis 28, prove that
lab
lab led
= 2 cos (a + B-Y)
(11)
Vab
Vcd Vab
с
+
= 2 cos (a + B - Y-).
If
- 9 hourbet
SYTU.. 2009​

Answer 1

Answer:

Given: A+B+C=π

L.H.S=cos2A+cos2B+cos2C

=[2cos(A+B)cos(A−B)]+(2cos

2

C−1)...cosC+cosD=2cos

2

C+D

cos

2

C−D

=2cos(180−C)cos(A−B)+2cos

2

C−1

=−2cosC(cos(A−B)−cosC)−1

=−2cosC(cos(A−B)+cos(A+B))−1

=−2cosC(2cosAcosB)−1

=−4cosAcosBcosC−1