Question

Choose the correct option and justify your choice : $\frac{1-{\tan }^{2}45°}{1+{\tan }^{2}45°}=?$

• A. $\tan 90°$
• B. $1$
• C. $\sin 45°$
• D. $0$

Answer 1

The correct option is D

$0$

Explaining the correct option:

We know from the trigonometry table that: $\tan 45°=1$

Putting this value in the given expression we get:

$$\begin{gathered} \Rightarrow \frac{1-{\tan }^{2}45°}{1+{\tan }^{2}45°}=\frac{1-{\left(1\right)}^2}{1+{\left(1\right)}^2} \\ \Rightarrow \frac{1-{\tan }^{2}45°}{1+{\tan }^{2}45°}=\frac{1-1}{1+1} \\ \Rightarrow \frac{1-{\tan }^{2}45°}{1+{\tan }^{2}45°}=0 \end{gathered}$$

Hence, the value of the given expression is $0$.