Prove that cosec y = cot y sec y?
- PopeLv 72 years agoBest Answer
That equation is not an identity, if that is what you mean.
Let y = 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.
- ComoLv 72 years ago
[ cos y / sin y ] [ 1 / cos y ] = 1 / sin y = cosec y____as required
- Raj KLv 72 years ago
cosec y = cot y sec y
RHS = cot y sec y
=1/siny=cosecy=LHS Hence proved
- cidyahLv 72 years ago
cosec y= 1/sin y
cot y sec y = (cos y/sin y)(1/cos y) = 1/sin y
LHS = RHS
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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)
- 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.