Question

prove sin theta/ theta =1​

Answer 1

Answer:

sin∅ /sin∅ = 1

as numerator and denominator both area same then answer will be 1

Answer 2

Hence it is proved that lim (x -> 0) sin theta/ theta = 1​

sin theta/ theta ≠ 1​

instead

lim (x -> 0) sin theta/ theta = 1​

Expansion of sin theta is given by,

sin theta = theta - theta^3/3!  + theta^5/5! - ..........

dividing both sides by theta, we get,

sin theta / theta  = 1 - theta^2/3!  + theta^4/5! - ..........

upon applying the lim (x -> 0)  on both sides, we get,

lim (x -> 0) sin theta / theta  = lim (x -> 0) (1 - theta^2/3!  + theta^4/5! - ..........)

lim (x -> 0) sin theta / theta  = 1 - 0 + 0 - ...............      (as lim (x -> 0) 1 = 1)

∴ lim (x -> 0) sin theta / theta  = 1