Question

prove that sin 5 theta divided by sin theta minus Cos 5 theta divided by cos theta equals to 4 cos 2 theta ​

Answer 1

Answer:

cos 2 theta=1

Step-by-step explanation:

i consider theta as A.

(sin5A/sinA)-(cos5A/cosA)=4

1st do LCM,

then you will get

sin5AcosA-cos5AsinA=4sinAcosA

use sin(A-B) formula...

sin(5A-A)=4sinAcosA

sin4A=4sinAcosA

use sin2A formula...

2sin2Acos24=4sinAcosA

again use sin2A formula...

4 sinA cosA cos2A=4sinAcosA

4sinAcosA(cos2A-1)=0

cos2A-1=0

cos2A=1