Question

express the trigonometric ratio sinA, sec A and tan A in terms of cot A

Answer 1

Identities Used:

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)