First slide

Trigonometric equations

Question

Number of values of $x \in [0, 5 π]$ and satisfying $\sin^{2} x = \cos^{2} x$ is

Moderate

A

5
B

10
C

20
D

40

Solution

$\begin{array}{l} \tan^{2} x = 1 \Rightarrow \tan x = \pm 1 \\ \tan x = 1 \Rightarrow x = \frac{π}{4}, \frac{5 π}{4}, \frac{9 π}{4}, \frac{13 π}{4}, \frac{17 π}{4} \end{array}$
and $\tan x = - 1 \Rightarrow x = \frac{3 π}{4}, \frac{7 π}{4}, \frac{11 π}{4}, \frac{15 π}{4}, \frac{19 π}{4}$
Thus, there are 10 values of $x .$

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