Trigonometric Fun

$\sin(A)=\cos(A)\to\dfrac{\sin(A)}{\cos(A)}=1\\ \tan(A)=1\to \tan^2(A)=1\to \tan(A)=\dfrac{1}{\tan(A)}\\ \boxed{\tan(A)=\cot(A)}$

$\sin A = \cos A$

$\frac{\sin A}{\cos A} = 1$

$\tan A = 1$

$\frac{1}{\tan A} = 1$

$\cot A = 1$

$\tan A = \cot A$

$\large \boxed{\text{If } \sin A = \cos A \text{ then } \tan A = \cot A}$

Solution: sinA = cosA => $\frac{orthographic}{hypotenuse}$ = $\frac{land}{hypotenuse}$ =>orthographic = land [each side divided by $\frac{1}{hypotenuse}$ ] [remember that,hypotenuse could never be 0]

   So, tanA = 1    [because orthographic = land, proved in previous(first) equation.]   
 And,cotA = 1   

   So,tanA = cotA 

      Ans: cotA .

if sin(A) = cos(A) definitely it will be a multiple of 45 or 225 so in that case definitely tan(A) = cot(A)

$\sin(A)=\cos(A)\rightarrow tan(A)=1, A=\frac{\pi}{4}+k\pi$ $\tan(A)=\frac{1}{\tan(A)}=\cot(A)$

You will get that $tan(a) = 1$ , and so as $\frac{1}{tan(a)} = cot(a) = 1$ . Note that $a = \frac{\pi}{4}, \frac{3\pi}{4}$