Given that tan x = 1, where 0 o ≥ x 90 o , evaluate 1-² x/ x

Correct Answer is : 22{{2}}{2}22

Correct Answer is : 22{{2}}{2}22

Test Index

WAEC Mathematics 2010 Paper

Question : 18

Total: 49

\geq

\frac{1-\sin^2 x}{\cos x}

Solution:

Concept:

Use the identity

1 - \sin^2 x = \cos^2 x

to simplify the expression, then find

\cos x

from

\tan x = 1

Explanation:

Given

\tan x = 1

and the angle is in the first quadrant,

0^\circ \le x \le 90^\circ

The angle whose tangent is

1

x = 45^\circ

Now simplify the expression:

\frac{1 - \sin^2 x}{\cos x} = \frac{\cos^2 x}{\cos x} = \cos x.

Substitute

x = 45^\circ

\cos 45^\circ = \frac{\sqrt{2}}{2}.

Thus the value is

\frac{\sqrt{2}}{2}

Answer:

\frac{\sqrt{2}}{2}

Option C.

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