Question

1. If secA = 1.25, find other trigonometric ratios.

2. If cosec4A = sec(A + 36o

), where 4A is an acute angle, find the value of A.
Please answer as fast as possible.
wrong answers will be reported.
It's urgent. ​

Answer 1

Step-by-step explanation:

We have,

sec A= 5/4

or, sec²A= 25/16

or, 1+tan²A= 25/16

or, tan²A= 25/16-1

or, tan²A= 9/16

or, tan A= 3/4.......(1)

now, sec A= 5/4

or, 1/cos A= 5/4

or, cos A= 4/5.....(2)

Multiplying (1) by (2) we get

tan A. cos A = 3/4 × 4/5

or, Sin A= 3/5.

Now, cosecA= 1/sin A= 5/3

cot A= 1/tanA= 4/3.

Hence

sinA= 3/5

cos A= 4/5

tan A= 3/4

cot A= 4/3

cosec A= 5/3.

2. We know that,

cosec (90°-A)=sec A

Therefore,

cosec 4A= sec(A+36°)

or, sec(90°-4A)=sec(A+36°)

or, 90°-4A= A+36°

or, 5A= 54°

or, A= 10.8°