Given that $sin θ - cos θ = 0$ , where $θ$ is the radian measure of an angle, which of the following could be true? $I . 0 < θ < \frac{π}{2}$ $I I . \frac{p i}{2} < θ < π$ $I I I . π < θ < \frac{3 π}{2}$

I

only

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I I

only

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I

and

I I I

only

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I

I I

, and

I I I

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Solution

The correct option is C $I$ and $I I I$ only
$sin x = cos x$
$\frac{sin x}{cos x} = 1$
$tan x = 1$
$x = {tan}^{- 1} (1) + x π$
$x = \frac{π}{4} + x π$
$n = 0, \frac{π}{4}$ $x = 1,$ $\frac{5 π}{4}$
$0 < \frac{π}{4} < \frac{π}{2}$ and $π < \frac{5 π}{4} < \frac{3 π}{2}$
$I$ and $I I I$

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θ

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