Question

If sin A= -8/17 and π<A<3π/2. Find the value of tan A- cos A / sec A + cosec A​

Answer 1

Answer:

Step-by-step explanation:

π<A<

3π

2

 

⇒A lies in 3rd quadrant,

sinA=-

4

5

 

⇒cosecA=

1

sinA

 

=-

5

4

 

cot2A=cosec2A-1

=(-

5

4

 

)2-1=

9

16

 

cotA=

3

4

 

(In 3rd quadrant, cot is positive)

∴tanA=

1

cotA

 

=

4

3

 

secA=

sinA

cosA

 

.

1

sinA

 

=tanA.cosecA

4

3

 

(-

5

4

 

)=-

5

3

 

Now  

cosecA+cotA

secA-tanA

 

=(-5/4)=-

5

3

 

Now  

cosecA+cotA

secA-tanA

 

=

-

5

4

 

+

3

4

 

-

5

3

 

-

4

3

 

 

=

-

2

4

 

-

9

3

 

 

=

1

6

 

Ans