Prove that 1-tan2A-1-cot2A - tan2A-

1+tan^2A/1+cot^2A =1+tan^2A/1 + 1/tan^2A =1+tan^2A/tan^2A+1/tan^2A =(1+tan^2A) (tan^2A)/(tan^2A+1) = tan^2A. ...

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Sin(A+B)Sin(A-B)

Prove that 1+...

Question

Prove that $\frac{1 + t a n^{2} A}{1 + c o t^{2} A}$ = $t a n^{2} A .$

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(\frac{1 + t a n^{2} A}{1 + c o t^{2} A}) = (\frac{1 - t a n A}{c o t A})^{2} = t a n^{2} A

\frac{1 - {t a n}^{2} A}{{c o t}^{2} A - 1} = {t a n}^{2} A

$\frac{1 + t a n^{2} A}{1 + c o t^{2} A}$ =

\frac{1 - {tan}^{2} A}{{cot}^{2} A - 1} = {tan}^{2} A

(s i n A + c o s e c A)^{2} + (c o s A + s e c A)^{2} = 7 + t a n^{2} A + c o t^{2} A .

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