if A is acute and 3 sin A = 4 cos A, find the value of 4 sin^2 A - 3 cos^A + 2
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1
Answer:
3cosA=4sinA
tanA=
4
3
tanA=
B
P
=
4
3
Now, Using Pythagoras Theorem,
H
2
=P
2
+B
2
H
2
=3
2
+4
2
H=5
Now, 4cos
2
A−3sin
2
A+2
= 4(
H
B
)
2
−3(
H
P
)
2
+2
= 4(
5
4
)
2
−3(
5
3
)
2
+2
=
25
64
−
25
27
+2
=
25
64−27+50
=
25
87
= 3
25
12
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