Question

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A .

Answer 1

An equation Involving trigonometric ratios of angle is called a trigonometry identity, if it is true for all values of the angles involved for any acute angle (A) we have 3 identities.

sin²A + cos²A= 1
1 + tan²A= sec²A
cot²A+ 1 = cosec²A

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Solution:

1)
sinA= 1/cosecA = 1 / √(1+cot²A)

[ cot²A+ 1 = cosec²A,
cosecA= √( 1+cot²A)]

2)
tanA= 1/cotA

3)
secA= √(1+tan²A)

[sec²A= 1+tan²A , secA= √ (1+tan²A)]

secA= √(1+ (1/cot²A)) = √ (1+1/ cot²A)
secA = √(cot²A+1/cot²A)

secA= √1+cot²A/ (cotA)


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Hope this will help you....

Answer 2

Answer:

1 + tan2 A = 1

sin2 A+cos2 A= 1

cot2 A + 1 = cosec2 A