Respuesta :

c. tan 75

Further explanation  

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

  • 1. solve the equation

[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]

  • 2. use the formula

[tex]\tt tan(a+b)=\dfrac{tan~a+tan~b}{1-tan~a.tan~b}\\\\tan(45+30)=tan~75[/tex]