If 3 cos θ = 5 sin θ , then the value of 5 sin θ - 2 sec³ θ + 2 cos θ/ 5 sin θ + 2 sec³ θ - 2 cos θ is
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Answer:
1
Step-by-step explanation:
cosθ=5sinθ
cosθ=(
3
5
)sinθ
cos
2
θ=(
3
5
)
2
sin
2
θ
1−sin
2
θ=(
9
25
)sin
2
θ
⇒sin
2
θ=
34
9
∴sinθ=
34
3
cos
2
θ=1−sin
2
θ=1−
34
9
=
34
25
∴cosθ=
34
5
∴
5sinθ−2sec
3
θ+2cosθ
5sinθ−2sec
3
θ+2cosθ
=
5×
34
3
−2×
125
34
34
+2×
34
5
5×
34
3
−2×
125
34
34
+2×
34
5
=
34
15
−2×
125
34
34
+
34
10
34
15
−2×
125
34
34
+
34
10
=
34
25
−2×
125
34
34
34
25
−2×
125
34
34
=1
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