c. tan 75
Trigonometry is the science of mathematics that studies the relationship between sides and angles in triangles
You can solve the equation or quickly use the existing formula
[tex]\tt \dfrac{tan~45+tan~30}{1-tan~45.tan~30}\\\\\dfrac{1+\dfrac{1}{3}\sqrt{3} }{1-1.\dfrac{1}{3}\sqrt{3} }\\\\\dfrac{1+\dfrac{1}{3}\sqrt{3} }{1-\dfrac{1}{3}\sqrt{3} }\times \dfrac{1+\dfrac{1}{3}\sqrt{3} }{1+\dfrac{1}{3}\sqrt{3} }\\\\\dfrac{1\dfrac{1}{3}+\dfrac{2}{3}\sqrt{3} }{\dfrac{3}{2} }\\\\2+\sqrt{3}=3.73=tan~75[/tex]
[tex]\tt tan(a+b)=\dfrac{tan~a+tan~b}{1-tan~a.tan~b}\\\\tan(45+30)=tan~75[/tex]