Write the expression sqareroot(x^2+4) in terms of Θ when x=2tanΘ?

Question

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Answer 1

2 secΘ....from trig you should remember that tan ² Θ + 1 = sec² Θ

Answer 2

substitute 2tan(theta) for x

and 1/cos(theta) for sqrt(1+tan^2(theta))

sqrt(4*tan^2(theta) + 4)

sqrt(4(1+tan^2(theta))

2*sqrt(1+tan^2(theta))

2 / cos(theta)  - theta between 0 and 90 and 270 and 360

-2 / cos(theta) - theta between 90 and 270