Answer:
[tex]tan157.5^{\circ}=-0.414[/tex]
Step-by-step explanation:
We are given that [tex]tan157.5^{\circ}[/tex]
We have to find the exact value of [tex]tan157.5^{\circ}[/tex] by using a half -angle identity.
We know that
[tex]tan\frac{\theta}{2}=\frac{1-cos\theta}{sin\theta}[/tex]
Therefore, we have
[tex]\frac{\theta}{2}=157.5^{\circ}[/tex]
[tex]\theta=157.5\times 2=315^{\circ}[/tex]
Now, by using half angle identity
[tex]\tan157.5^{\circ}=\frac{1-cos315^{\circ}}{sin315^{\circ}}[/tex]
[tex]\tan157.5^{\circ}=\frac{1-0.707}{-0.707}[/tex]
[tex]tan157.5^{\circ}=-0.414[/tex]
