Math, asked by mohdkaif8172, 9 months ago

If tanA=cosA then find the value of(sinA+cosecA)²+(cosA+secA)10

Answers

Answered by rinkukumar08r3
0

Step-by-step explanation:

MATHS

If 4sinA−3cosA=0, find sinA,cosA,secA and cosec A.

December 26, 2019avatar

Saummya Achu

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ANSWER

Let △PQR be a right angled triangle where ∠Q=90

0

and ∠R=A as shown in the above figure:

Now it is given that 4sinA−3cosA=0 that is

4sinA=3cosA

cosA

sinA

=

4

3

⇒tanA=

4

3

We know that, in a right angled triangle, tanθ is equal to opposite side over adjacent side that is tanθ=

Adjacentside

Oppositeside

, therefore, opposite side PQ=3 and adjacent side QR=4.

Now, using pythagoras theorem in △PQR, we have

PR

2

=PQ

2

+QR

2

=3

2

+4

2

=9+16=25

⇒PR=

25

=5

Therefore, the hypotenuse PR=5.

We know that, in a right angled triangle,

sinθ is equal to opposite side over hypotenuse that is sinθ=

Hypotenuse

Oppositeside

and

cosθ is equal to adjacent side over hypotenuse that is cosθ=

Hypotenuse

Adjacentside

Here, we have opposite side PQ=3, adjacent side QR=4 and the hypotenuse PR=5, therefore, the trignometric ratios of angle A can be determined as follows:

sinA=

Hypotenuse

Oppositeside

=

PR

PQ

=

5

3

cosA=

Hypotenuse

Adjacentside

=

PR

QR

=

5

4

cosec A=

sinA

1

=

5

3

1

=1×

3

5

=

3

5

secA=

cosA

1

=

5

4

1

=1×

4

5

=

4

5

Hence, sinA=

5

3

, cosA=

5

4

, cscA=

3

5

and secA=

4

5

.

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