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Question

need help proving/verifying the identity to the problem sin (x-y)/cos x sin y =tanx coty - 1.

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Statement
Rule
PROVE THE IDENTITY
Sin (x-y)
cos x sin y
= tan x coty - 1
We start by manipulating the
left-hand side. (LHS)
sin x cos y - cos x sin y
= tan x coty -
Here we can use Ptolemy
cos x sin y
theorem/ Sum and
Difference to multiply x - y.
sin x cos y
cos x sin y
To simplify the proof, we use
cos x sin y
cos x sin y
tan x coty - 1
the Algebra rule, to separate
left side of equation into two
parts.
sin x cos y
1 = tan x coty - 1
Simplify the expression using
cos x sin y
the rule of Algebra.
cos x sin y
cos x sin y
cos y
tan x-
Here we substitute the
sin y
1 = tan x cot y - 1
quotient value using the
Quotient Identity-
tanx =
cos y
sin y
Etan x coty - 1 = tan xcoty - 1 -
process as the previous step
by substituting the quotient
value cot y
cosy
sin y
using the
Quotient Identity.

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Subject: Calculus, Math

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