If sin theta=1/2 then show that 3 cos theta minus 4 cos cubed theta equals 0

Asked by shreya ghoshal | 16th Oct, 2014, 06:18: AM

Expert Answer:

G i v e n space t h a t space sin theta equals 1 half rightwards double arrow sin theta equals sin 30 degree rightwards double arrow theta equals 30 degree N o w space c o n s i d e r space t h e space L e f t space h a n d space s i d e space o f space t h e space e q u a t i o n comma space 3 cos theta minus 4 cos cubed theta : W e space k n o w space t h a t comma space cos 3 theta equals 4 cos cubed theta minus 3 cos theta T h u s comma space 3 cos theta minus 4 cos cubed theta equals minus open parentheses 4 cos cubed theta minus 3 cos theta close parentheses space space space space space space space space space space space space space space space space space space space space space space space equals minus cos 3 theta space space space space space space space space space space space space space space space space space space space space space space space equals minus cos open parentheses 3 cross times 30 degree close parentheses space space space space space space space space space space space space space space space space space space space space space space space equals minus cos open parentheses 90 degree close parentheses space space space space space space space space space space space space space space space space space space space space space space space equals 0 H e n c e space p r o v e d.

Answered by Vimala Ramamurthy | 16th Oct, 2014, 08:57: AM