Question

Express the Write all the other trigonometric ratios of ∠ A in terms of sec A. 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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