the value of expression (sin theta / cot theta + cosec theta - sin theta / cot theta - cosec theta) is a) - 2 b)-1 c) 1 d) 2
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Step-by-step explanation:
Given θ=3α and
sinθ=
a
2
+b
2
a
⇒a=
a
2
+b
2
sinθ then
cosθ=
a
2
+b
2
b
⇒b=
a
2
+b
2
cosθ
acscα−bsecα=
sinα
a
−
cosα
b
=
sinα
a
2
+b
2
sinθ
−
cosα
a
2
+b
2
cosθ
=(
a
2
+b
2
)(
sinα
sinθ
−
cosα
cosθ
)
=(
a
2
+b
2
)
sinαcosα
sinθcosα−cosθsinα
=(
a
2
+b
2
)
sinαcosα
sin(θ−α)
since sinAcosB−cosAsinB=sin(A−B)
=(
a
2
+b
2
)
sinαcosα
sin(3α−α)
where θ=3α
=(
a
2
+b
2
)
sinαcosα
sin2α
=(
a
2
+b
2
)
sinαcosα
2sinαcosα
=2
a
2
+b
2
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