cot⁡θ=sin⁡2θ, θ≠nπ, n∈Z, if θ equals - Infinity Learn by Sri Chaitanya

A
$45^{\circ} or 90^{\circ}$
B
$45^{\circ} or 60^{\circ}$
C
$90^{\circ}$ only
D
$45^{\circ}$ only

Solution:

We have

$\begin{array}{l} \cot θ = \sin 2 θ \\ \Rightarrow \cos θ = 2 \sin^{2} θ \cos θ \\ \Rightarrow \cos θ (1 - 2 \sin^{2} θ) = 0 \\ \Rightarrow \cos θ = 0 or, 1 - 2 \sin^{2} θ = 0 \\ \Rightarrow \cos θ = 0 or, \sin^{2} θ = {(\frac{1}{\sqrt{2}})}^{2} \\ \Rightarrow θ = 90^{\circ} or θ = 45^{\circ} \end{array}$

$\cot θ = \sin 2 θ, θ \neq n π, n \in Z,$ if $θ$ equals

Solution:

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