First slide

Trigonometric Identities

Question

Which of the following is possible?

Very Easy

A

$\sin θ = a + \frac{1}{a}, a \neq 0$
B

$\tan θ = 2019^{2020}$
C

$\cos θ = \frac{1 + p^{2}}{1 - p^{2}}, p \neq 0$
D

$s e c θ = \frac{1}{2}$

Solution

$a + \frac{1}{a} \geq 2 o r \leq - 2; \sin θ a n d \cos θ r a n g e i s [- 1, 1]$
$1 + p^{2} \geq 1 - p^{2}; s e c θ c a n n o t b e l e s s t h a n 1$
range of $\tan θ$ is set of real numbers
$∴$ option B is true

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