SOLUTION: Given that x = a tan tita simplify sqrt( 1 + x^2 / a^2 )

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Question 1134558: Given that x = a tan tita
simplify
sqrt( 1 + x^2 / a^2 )
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Makes no sense.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given  x = a%2Atan%28theta%29.


Then  1+%2B+x%5E2%2Fa%5E2%29 = 1+%2B+%28a%5E2%2Atan%5E2%28theta%29%29%2Fa%5E2 = 1+%2B+tan%5E2%28theta%29 = 1+%2B+sin%5E2%28theta%29%2Fcos%5E2%28theta%29 = %28cos%5E2%28theta%29+%2B+sin%5E2%28theta%29%29%2Fcos%5E2%28theta%29 = 1%2Fcos%5E2%28theta%29.


Therefore,  sqrt%281+%2B+x%5E2%2Fa%5E2%29 = sqrt%281%2Fcos%5E2%28theta%29%29 = 1%2Fcos%28theta%29.


The sign of the resulting expression follows the sign of cos%28theta%29 in its quadrant.