if sin a = 1/3 then find the value of cos a,cosec a + tan a and sec a
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Answer:
If sin A = 1/3, then evaluate cos A . cosec A + tan A . sec A
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Step-by-step explanation:
sinA=
3
1
Now we will construct a triangle ABC in which ∠B=90
∘
and BC:AC=1:3
Let BC=k and AC=3k where k>0 which is a constant quantity.
∴ From Baudhayana Formula
AC
2
=AB
2
+BC
2
AB
2
=AC
2
−BC
2
=(3k)
2
−(k)
2
=9k
2
−k
2
=8k
2
⇒ AB=±2
2
Since ∠A is acute therefore AB will be +ve.
∴ cosA=
AC
AB
=
3k
2
2
k
=
2
2
3
cosec A=3
tanA=
AB
BC
=
2
2
k
k
=
2
2
1
secA=
cosA
1
=
2
2
3
∴ According tp question the value of
cosA.cosec A+tanA.secA
=
3
2
2
×3+
2
2
1
×
2
2
3
=2
2
+
8
3
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