Given that tan x = 1, where 0o (geq) x 90o, evaluate (frac{1 – sin^2 x}{cos x})
-
A.
2(sqrt{2}) -
B.
(sqrt{2}) -
C.
(frac{sqrt{2}}{2}) -
D.
(frac{1}{2})
Correct Answer: Option C
Explanation
Given tan x = 1
x = tan-1(1)
x = 45o
Now, (frac{1 – ( frac{1}{sqrt{2} )^2}}{frac{1}{sqrt{2}}})
= (frac{1 – frac{1}{2}}{frac{1}{2}})
= (frac{1}{2} + frac{1}{sqrt{2}})
= (frac{1}{2} times frac{1}{sqrt{2}})
= (frac{sqrt{2}}{2})