Math, asked by uttamkumargupta71, 4 months ago

if sin a = 1/3 then find the value of cos a,cosec a + tan a and sec a​

Answers

Answered by shraddha837
0

Answer:

If sin A = 1/3, then evaluate cos A . cosec A + tan A . sec A

Attachments:
Answered by bhoomikatavarageri
0

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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