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Mathematics
Mathematics
Problem
(a) State the algebraic relation between
sin
2
A
\sin^2 A
sin
2
A
and
cos
2
A
\cos^2 A
cos
2
A
for any acute angle
A
A
A
. (b) Prove that
1
−
sin
2
A
cos
2
A
=
1
\dfrac{1 - \sin^2 A}{\cos^2 A} = 1
cos
2
A
1
−
sin
2
A
=
1
for an acute angle
A
A
A
. (c) Hence, show that
(
1
−
sin
A
)
(
1
+
sin
A
)
=
cos
2
A
(1 - \sin A)(1 + \sin A) = \cos^2 A
(
1
−
sin
A
)
(
1
+
sin
A
)
=
cos
2
A
.
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