Question

express the trignometry ratios sinA and secA in terms of cot A

Answer 1

~Sin A

sin A/Cos A = tan A
Sin A = tan A cos A

Sin A = tan A (1/ sec A)

tan² A + 1 = Sec² A
=> Sec² A =+- √[tan²A +1]

Substitute in Sin equation

Sin A = tan A {1/[+-√(tan²A +1)]}

Sin A= tan A/+-√[tan² A +1]

tan A = 1/Cot A

Substitute in Sin equation

Sin A =(1/cot A)/+-√[(1/cot A)²+1]

Simplify

Sin A = {(1/cot A)}/{+-√(1+cot²A)/cot A}