# Prove that cosec y = cot y sec y?

### 6 Answers

- PopeLv 72 years agoBest Answer
That equation is not an identity, if that is what you mean.

Let y = π/2.

LHS

= csc(y)

= csc(π/2)

= 1

RHS

= cot(y)sec(y)

= cot(π/2)sec(π/2)

The secant function is undefined at π/2.

An undefined expression has been equated with 1. The equation is not an identity. Having no information on the value of y, the equation cannot be proved.

- Raj KLv 72 years ago
cosec y = cot y sec y

RHS = cot y sec y

=(cosy/siny)(1/cosy)

=1/siny=cosecy=LHS Hence proved

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- BrainardLv 72 years ago
LHS = cosec(y) = 1/sin(y)

= 1/sin(y) * cos(y)/cos(y)

= cos(y)/sin(y) * 1/cos(y)

= cot(y) sec(y)

= RHS

- az_lenderLv 72 years ago
cosec(y) = 1/sin(y);

and on the right-hand side,

cot(y)sec(y) = [cos(y)/sin(y)]*[1/cos(y)] = 1/sin(y),

the same as the left-hand side.