Question

If sin a =3/5 find the value of tan^2a+sin@ cos@ +cot@

Answer 1

Answer:

24/7

Step-by-step explanation:

Use the trig identity:

tan

2

A

=

2

tan

A

1

−

tan

2

A

(

1

)

.

First, find

tan

A

=

sin

A

cos

A

.

sin

A

=

3

5

-->

sin

2

A

=

9

25

-->

cos

2

A

=

1

−

9

25

=

15

25

-

-->

cos

A

=

±

4

5

.

Because A is in Quadrant II, its cos is negative.

cos

A

=

−

4

5

tan

A

=

sin

A

cos

A

=

(

3

5

)

(

−

5

4

)

=

−

3

4

Replace value of tan A = -3/4 into identity (1) -->

tan

2

A

=

−

3

2

1

−

9

16

=

(

−

3

2

)

(

16

7

)

=

−

24

7

Check by calculator.

cos

A

=

−

4

5

=

−

0.8

-->

A

=

143.13

-->

2

A

=

286.26

.-->

->

tan

2

A

=

−

3.43

−

24

7

=

−

3

.

43

.

OK