By writing JA for in cot^2 +1=cosec^2 determine the corresponding hyperbolic identify
The trick you need here is to change every term containing sin^2 to -sinh^2
(after converting it so it contains sin's and cos's only) in a trig identity to get
the corresponding hyperbolic identity.
So
cot^2 +1=cosec^2
becomes:
sin^2/cos^2 + 1 = 1/sin^2.
So the corresponding hyperbolic identity is:
-sinh^2 / cosh^2 + 1 = -1/sinh^2
or:
-tanh^2 + 1 = -cosech^2
or:
tanh^2 -1 = cosech^2
RonL
Hello, gracy!
Two questions: What is "JA"? .And do they really expect us to know
. . conversions between circular and hyperbolic trig?
By writing in JA for: cot²x + 1 .= .csc²x
determine the corresponding hyperbolic identify.
I would begin with the first identity of hyperbolics: .cosh²x - sinh²x .= .1
. . . . . . . . . . . . . .cosh²x . .sinh²x . . . . . .1
Divide by sinh²x: . --------- - -------- .= . --------
. . . . . . . . . . . . . .sinh²x . . sinh²x . . . .sinh²x
. . and we get: .coth²x - 1 .= .csch²x