If 3 cosA = 4 sinA, find the value of:
i) 3- cot 2A+cosec2A
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Answer:
3cosA=4sinA
tanA=
4
3
tanA=
B
P
=
4
3
Using Pythagoras Theorem,
H
2
=P
2
+B
2
H
2
=3
2
+4
2
H
2
=5
2
H=5
Now, 3−cot
2
A+csc
2
A = 3−(
P
B
)
2
+(
P
H
)
2
= 3−(
3
4
)
2
+(
3
5
)
2
= 3−
9
16
+
9
25
=
9
27−16+25
=
9
36
= 4
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