Question

cosecA-cotA=4/5
find numeric value of cosecA in fraction form​

Answer 1

Answer:

41/40

Step-by-step explanation:

See the image...

Answer 2

Trigonometry: Trigonometry is the study of angles and relations between angles and their sin, cos, tan, cosec, sec, cot ratios. There are many formulae for calculations:

• sin²A + cos²A = 1

• sec²A - tan²A = 1

• cosec²A - cot²A = 1

• sin2A = 2 sinA cosA

• cos2A = cos²A - sin²A

• tan2A = 2 tanA / (1 - tan²A)

SOLUTION:

Given, cosecA - cotA = 4/5 ..... (1)

We know that,

cosec²A - cot²A = 1

or, (cosecA - cotA) (cosecA + cotA) = 1

or, 4/5 * (cosecA + cotA) = 1, by (1)

or, cosecA + cotA = 5/4 ..... (2)

Adding (1) and (2), we get

cosecA - cotA + cosecA + cotA = 4/5 + 5/4

or, 2 cosecA = (16 + 25)/20

or, cosecA = 41/40

∴ cosecA = 41/40