prove that Sin A + Cos A divided by Sin A minus Cos A + Sin A minus Cos A divided by sin a + cos A is equal to 2 by 2 sin square A minus one
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1
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Given,
sinA=
13
12
We know that,
sinA=
Hypotenuse
oppositeSide
From Pythagoras theorem,
(Hypotenuse)
2
=(oppositeSide)
2
+(adjacentSide)
2
13
2
=12
2
+(adjacentSide)
2
(adjacentSide)
2
=169−144=25
(adjacentSide)=5
cosA=
Hypotenuse
AdjacentSide
=
13
5
tanA=
AdjacentSide
OppositeSide
=
5
12
Therefore,
2sinθcosθ
sin
2
θ−cos
2
θ
×
tan
2
θ
1
=
2(
13
12
)(
13
5
)
(
13
12
)
2
−(
13
5
)
2
×
(
5
12
)
2
1
=
2(
13
12
)(
13
5
)
(
169
144
)−(
169
25
)
×
144
25
=
(
169
120
)
(
169
144−25
)
×
144
25
=
120
119
×
144
25
=
24
119
×
144
5
=
3456
595
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4
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