Question

Prove that:
sin²A+1/(1+Tan²A)=1​

Answer 1

Answer:

Prove that:

sin²A+1/(1+Tan²A)=1

Answer 2

Answer:

$\frac{\sin ^2\left(A\right)+1}{\left(1+\tan ^2\left(A\right)\right)}=1\quad :\quad \begin{bmatrix}\mathrm{Radians:}\:&\:A=2\pi n,\:A=\pi +2\pi n\:\\ \:\mathrm{Degrees:}&\:A=0^{\circ \:}+360^{\circ \:}n,\:A=180^{\circ \:}+360^{\circ \:}n\end{bmatrix}$

Step-by-step explanation:

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

$\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$

$\frac{\sin ^2\left(A\right)+1}{1+\tan ^2\left(A\right)}-1=0$

$\frac{\sin ^2\left(A\right)-\tan ^2\left(A\right)}{1+\tan ^2\left(A\right)}=0$

$\frac{f\left(x\right)}{g\left(x\right)}=0\quad \Rightarrow \quad f\left(x\right)=0$

$\sin ^2\left(A\right)-\tan ^2\left(A\right)=0$

$\left(\sin \left(A\right)+\tan \left(A\right)\right)\left(\sin \left(A\right)-\tan \left(A\right)\right)=0$

$\mathrm{Solving\:each\:part\:separately}$

$\sin \left(A\right)+\tan \left(A\right)=0\quad \mathrm{or}\quad \sin \left(A\right)-\tan \left(A\right)=0$

$\mathrm{Combine\:all\:the\:solutions}$

$A=2\pi n,\:A=\pi +2\pi n$