Question

Tan45+tan30/ 1- tan45.tan30 is equivalent to

a) tan90
b)sin45/cos30
c)tan75
d)tan15
can you explain the solution thanks​

Answer 1

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

`\tt (tan~45+tan~30)/(1-tan~45.tan~30)\\\\(1+(1)/(3)√(3) )/(1-1.(1)/(3)√(3) )\\\\(1+(1)/(3)√(3) )/(1-(1)/(3)√(3) )* (1+(1)/(3)√(3) )/(1+(1)/(3)√(3) )\\\\(1(1)/(3)+(2)/(3)√(3) )/((3)/(2) )\\\\2+√(3)=3.73=tan~75`

• 2. use the formula

`\tt tan(a+b)=(tan~a+tan~b)/(1-tan~a.tan~b)\\\\tan(45+30)=tan~75`