Given that tan x = 1, where 0 o \(\geq\) x 90 o , evaluate
MATHEMATICS
WAEC 2010
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: C. \(\frac{\sqrt{2}}{2}\)
Explanation
Given tan x = 1
x = tan-1(1)
x = 45o
Now, \(\frac{1 - ( \frac{1}{\sqrt{2} )^2}}{\frac{1}{\sqrt{2}}}\)
= \(\frac{1 - \frac{1}{2}}{\frac{1}{2}}\)
= \(\frac{1}{2} + \frac{1}{\sqrt{2}}\)
= \(\frac{1}{2} \times \frac{1}{\sqrt{2}}\)
= \(\frac{\sqrt{2}}{2}\)
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