If 3 cot A = 4, check whether
1- tan²A
cos2 A-sin? A is true or not.
1 + tan2A
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Answer:
Given,
3cotA=4
sinA=
AC
BC
cosA=
AC
AB
tanA=
AB
BC
cotA=
BC
AB
=
3k
4k
AB=4k
BC=3k
By pythagoras Theorem we get,
AC
2
=AB
2
+BC
2
AC
2
=4
2
+3
2
AC
2
=16+9
AC
2
=25
AC
2
=
2
5
AC=5k
L.H.S
=
1+tan
2
A
1−tan
2
A
=
1+(
4
3
)
2
1−(
4
3
)
2
=
1+
16
9
1−
16
9
=
16+9
16−9
=
25
7
R.H.S
=cos
2
A−sin
2
A
=(
5
4
)
2
−(
5
3
)
2
=
25
16
−
25
9
=
25
7
Hence,
L.H.S=R.H.S proved.
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