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If sin(6/5x) = 0 and cos (x/5) = 0 , the...

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`

Text Solution

Verified by Experts

The correct Answer is:
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`
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