Question

If `sin(6/5x) = 0` and `cos (x/5) = 0` , then
A. `x = (n-5)pi`
B. `x=6(n-1)pi`
C. `x=5(n-(1)/(2))pi`
D. `x=5(n+(1)/(2))pi`

Answer 1

Correct Answer - C::D
(a) is false since `cos(n-5)(pi)/(5)ne 0` for all integers n.
(b) is false since `sin.(6)/(5).6(n-1)pi ne0` for all integers n.
(c ) is correct since `sin.(6)/(5)x=sin (6n-3)pi=0`
Also `cos.(x)/(5)=cos(n-(1)/(2))pi=cos(2n-1)(pi)/(2)=0`
(d) is also correct since `sin.(6)/(5)x=sin (6n+3)pi =0`
Also `cos.(x)/(5)=cos(n+(1)/(2))pi=cos (2n+1)(pi)/(2)=0`