Question

I'd sin A= 3/5, cosB= 1/3, find tan(A-B)

Answer 1

Answer:

First, find tan A and tan B.

cos

A

=

3

5

-->

sin

2

A

=

1

−

9

25

=

16

25

-->

cos

A

=

±

4

5

cos

A

=

4

5

because A is in Quadrant I

tan

A

=

sin

A

cos

A

=

(

4

5

)

(

5

3

)

=

4

3

.

sin

B

=

5

13

-->

cos

2

B

=

1

−

25

169

=

144

169

-->

sin

B

=

±

12

13

.

sin

B

=

12

13

because B is in Quadrant I

tan

B

=

sin

B

cos

B

=

(

5

13

)

(

13

12

)

=

5

12

Apply the trig identity:

tan

(

A

−

B

)

=

tan

A

−

tan

B

1

−

tan

A

.

tan

B

tan

A

−

tan

B

=

4

3

−

5

12

=

11

12

(

1

−

tan

A

.

tan

B

)

=

1

−

20

36

=

16

36

=

4

9

tan

(

A

−

B

)

=

(

11

12

)

(

9

4

)

=

33

16

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