Prove that: -1+sin〖A sin(90°-A) 〗/cot(90°-A) =-〖sin〗^2 A.
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Prove that
cos
(
90
−
A
)
⋅
sin
(
90
−
A
)
tan
(
90
−
A
)
=
sin
2
A
.
Solution
cos
(
90
−
A
)
=
sin
(
A
)
;
sin
(
90
−
A
)
=
cos
(
A
)
;
tan
(
90
−
A
)
=
cot
(
A
)
cot
(
A
)
=
cos
(
A
)
sin
(
A
)
LHS
cos
(
90
−
A
)
sin
(
90
−
A
)
tan
(
90
−
A
)
=
sin
(
A
)
cos
(
A
)
cot
(
A
)
sin
(
A
)
cos
(
A
)
cot
(
A
)
=
sin
(
A
)
cos
(
A
)
sin
(
A
)
cos
(
A
)
sin
(
A
)
cos
(
A
)
sin
(
A
)
cos
(
A
)
=
sin
(
A
)
sin
(
A
)
=
sin
2
(
A
)
=
L
H
S
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