Question

True or False$\tan {75}^{\mathrm{o}}=\tan {30}^{\mathrm{o}}+\tan {45}^{\mathrm{o}}$

Short answer

$\tan {75}^{\mathrm{o}}=\tan {30}^{\mathrm{o}}+\tan {45}^{\mathrm{o}}$is false.

Step-by-step solution

Step 1. Given information 

Given that $\tan {75}^{\mathrm{o}}=\tan {30}^{\mathrm{o}}+\tan {45}^{\mathrm{o}}$.

We have to tell whether this is true or false.

Step 2. Apply the sum formula

We know $\tan (\alpha +\beta )=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }$.

We can write ${75}^o={30}^o+{45}^o$.

$\tan ({30}^o+{45}^o)=\frac{\tan {30}^o+\tan {45}^o}{1-\tan {30}^o\tan {45}^o}$

Therefore, $\tan {75}^{\mathrm{o}}=\tan {30}^{\mathrm{o}}+\tan {45}^{\mathrm{o}}$is false.