If Sin theta = a/b, then find the value of sec theta + tan theta

Question

please describe whole process

Answer 1

secθ + tanθ = 1/cosθ + sinθ/cosθ = (1 + sinθ)/cosθ

 

sinθ = a/b and cosθ = [√(b² - a²)] /b

 

Therefore (1 + sinθ)/cosθ = (1 + a/b) / (√(b² - a²)) /b

 

= (b+a)/b / √(b² - a²)/b

 

= (b+a)/√(b² - a²)

Answer 2

sinΘ=Opposite/Hypotenuse. So a=Opposite, and b=Hypotenuse, well call c=Adjacent where c=sqrt(b²-a²) because of the Pythagorean theorem. secΘ=H/A=b/c and tanΘ=O/A=a/c, where the capital letters refer to the general terms and the lower case letters refer to this problem.

 

secΘ+tanΘ=                                         replace with components determined above

(b/c)+(a/c)=                                        combine numerators over common denominator

(b+a)/c=                                              replace c with its equal in terms of a and b, so that the answer is using the variables give (a and b)

(b+a)/{sqrt(b2-a2)}=     answer