Question

13) Prove that, 1−tan 45 / 1+tan 45

= 0.​

Answer 1

Given

$\rm \dfrac{1-tan\ 45}{1+tan\ 45}$

To Prove

$\rm \dfrac{1-tan\ 45}{1+tan\ 45}=0$

Formula Applied

$\rm tan\ 45=\dfrac{sin\ 45}{cos\ 45}\\\\\to \rm tan\ 45=\dfrac{\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}}\\\\\to \bf tan\ 45=1$

$\bf \dfrac{0}{n}=0$

where , n ≠ 0

Solution

$\rm \dfrac{1-tan\ 45}{1+tan\ 45}\\\\\to \rm \dfrac{1-1}{1+1}\\\\\to \rm \dfrac{0}{2}\\\\\to \bf 0\\\\\bf RHS$

Hence proved

Answer 2

Answer:

Given

$\rm \dfrac{1-tan\ 45}{1+tan\ 45} </p><p>$

To Prove

Formula Applied

$\begin{gathered}\rm tan\ 45=\dfrac \pink{sin\ 45}{cos\ 45}\\\\\to \rm tan\ 45=\dfrac{\frac{1} \red{\sqrt{2}}}{\frac \green{1}{\sqrt{2}}}\\\\\to \bf tan\ 45=1\end{gathered} </p><p>$

$\bf \dfrac{0}{n}=0$

where , n ≠ 0

Solution

$</p><p>\begin{gathered}\rm \dfrac \blue{1-tan\ 45} \red{1+tan\ 45}\\\\\to \rm \dfrac \pink{1-1} \red{1+1}\\\\\to \rm \dfrac{0}{2}\\\\\to \bf 0\\\\\bf RHS\end{gathered}$

Hence proved