Question

Express the trigonometric ratios sinA , secA and tanA in terms of cotA.​

Answer 1

hope this helps u

tanA=sinA/cosA  

cotA=cosA/sinA  

therefore tanA=1/cotA  

using the identity cosec^2A-cot^2A=1  

we get cosec^2A=1+cot^2a  

1/sin^2A=1+cot^2A  

sin^2A=1/1+cot^2A  

sinA=(1/1+cot^2A)^1/2  

using identity sec^2A-tan^2A=1  

we get  

sec^2A=1+tan^2A  

sec^2A=1+1/cot^2A  

sec^2A=cot^2A+1/cot^2A  

secA=(cot^2A+1/cot^2A)^1/2

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Answer 2

$\bold {cosec²A - cot²A = 1}$

$\implies cosec²A = 1 + cot²A$

$\implies sin²A = (\frac{1}{1+cot²A})$

$\implies sinA = ± \sqrt { (\frac{1}{1+cot²A})}$

Now ,

$\implies sin²A = (\frac {1}{1+cot²A})$

$\implies 1-cos2A = (\frac{1}{cot²A})$

$\implies cos²A=1-(\frac{1}{1+cot²A})$

$\implies cos²A = (\frac {cot²A}{1+cot²A})$

$\implies sec²A = (\frac{1+cot²A}{cot²A}) = 1 + (\frac{1}{cot²A})$

$\implies secA = ± \sqrt {1+(\frac{1}{cot²A})}$

And , tanA. cotA $= 1$

$\implies tanA = (\frac{1}{cotA})$