If cos(theta) = (frac{a}{b}), find 1 + tan2(theta)
-
A.
(frac{b^2}{a^2}) -
B.
(frac{a^2}{b^2}) -
C.
(frac{a^2 + b^2}{b^2 – a^2}) -
D.
(frac{2a^2 + b^2}{a^2 + b^2})
Correct Answer: Option A
Explanation
cos(theta) = (frac{a}{b}), Sin(theta) = (sqrt{frac{b^2 – a^2}{a}})
Tan(theta) = (sqrt{frac{b^2 – a^2}{a^2}}), Tan 2 = (sqrt{frac{b^2 – a^2}{a^2}})
1 + tan2(theta) = 1 + (frac{b^2 – a^2}{a^2})
= (frac{a^2 + b^2 – a^2}{a^2})
= (frac{b^2}{a^2})