NDA2010MathematicsTrigonometric Ratios & IdentitiesActual
If angles A , B , C are in AP , then what is A+2 B+ C equal to?
Options
- A4 ~B ^2 ( ~A - C 2 )
- B4 ~B ^2 ( ~A - C 4 )
- C4 (2 B) ^2 ( A-C 2 )
- D4 (2 B) ^2 ( A-C 4 )
Correct answer
B. 4 ~B ^2 ( ~A - C 4 )
Step-by-step solution
aligned & A + C +2 ~B & =2 ( ~A + C 2 ) ( A - C 2 )+2 ~B & =2 ~B ( A-C 2 )+2 ~B & =2 ~B [1+ ( A - C 2 ) ] & =4 ~B ^2 ( ~A - C 4 ) aligned