Question

Express the trigonometric ratios sinA secA and tanA in terms of cot A

Answer 1

sin²A + cos²A= 1
1 + tan²A= sec²A
cot²A+ 1 = cosec²A
tanA= 1/cotA

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)