Is (tan^2(A))/(tan^2(A)+1)=sin^2(A) ?

The answer to whether (tan^2(A))/(tan^2(A)+1)=sin^2(A) is True

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prove (tan^2(A))/(tan^2(A)+1)=sin^2(A)

prove

\frac{tan ^{2} ( A )}{tan ^{2} ( A ) + 1} = sin^{2} (A)

True

Solution steps

\frac{tan ^{2} ( A )}{tan ^{2} ( A ) + 1} = sin^{2} (A)

Manipulating left side

\frac{tan ^{2} ( A )}{tan ^{2} ( A ) + 1}

Express with sin, cos

= \frac{sin ^{2} ( A )}{cos ^{2} ( A ) + sin ^{2} ( A )}

Rewrite using trig identities

= sin^{2} (A)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sec ^{4} ( α ) - 1}{tan ^{2} ( α )} = sec^{2} (α) + 1

\frac{1 + sec ( x )}{csc ( x )} - tan (x) = sin (x)

2 sin (x) = \frac{4 cos ( x ) - 1}{tan ( x )}

cos (8 x) = cos^{2} (4 x) - sin^{2} (4 x)

tan (\frac{π}{2} - x) cot (x) = csc^{2} (x) - 1

Is (tan^2(A))/(tan^2(A)+1)=sin^2(A) ?
The answer to whether (tan^2(A))/(tan^2(A)+1)=sin^2(A) is True