If tan x = 1, evaluate sin x + cos x, leaving your answer in
MATHEMATICS
WAEC 2008
If tan x = 1, evaluate sin x + cos x, leaving your answer in the surd form
- A. 2\(\sqrt{2}\)
- B. \(\frac{1}{2} \sqrt{2}\)
- C. \(\sqrt{2}\)
- D. 2
Correct Answer: C. \(\sqrt{2}\)
Explanation
tan x = 1; x = tan-1(10 = 45o
sin x + cos x
= sin 45o + cos 45o
= \(\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}\)
= \(\frac{\sqrt{2} + \sqrt{2}}{2}\)
= \(\frac{2\sqrt{2}}{2}\)
= \(\sqrt{2}\)
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