Find the principal solutions of =0. - Vidyadip

Question

Find the principal solutions of $\cot \theta=0$.

✓

Answer

$\cot \theta=0 $
$\Rightarrow \tan \theta$ is not defined.
But $\tan \frac{\pi}{2}$ is not defined.
$\therefore \tan \theta=\tan \frac{\pi}{2}, $
$\therefore \theta=\frac{\pi}{2}$
$\text { Also } \tan \frac{\pi}{2}=\tan \left(\pi+\frac{\pi}{2}\right)=\tan \frac{3 \pi}{2}$
$\therefore 0 \leq \frac{\pi}{2} \leq 2 \pi \text { and } 0 \leq \frac{3 \pi}{2} \leq 2 \pi \text {. }$
$\therefore$ Principal solutions are $\theta=\frac{\pi}{2}$ and $\theta=\frac{3 \pi}{2}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\tan^3\text{x}\sec^2\text{x}\text{dx}$

Let X be the amount of time for which a book is taken out of the library by a randomly selected students and suppose X has p.d.f.
f(x) = 0.5x, for 0 ≤ x ≤ 2 and = 0 otherwise.
Calculate:
P(x ≤ 1)

If $\begin{bmatrix}\text{a+b}&2\\5&\text{b} \end{bmatrix}=\begin{bmatrix}6&5\\2&2 \end{bmatrix}$, then find a.

Find the values of the following:
$\cos\big(\sec^{-1}\text{x}+\text{cosec}^{-1}\text{x}\big),|\text{x}|\geq1$

Find the approximate values of :

$\log _e(9.01)$, given that $\log 3=1.0986$.

Evaluate the following determinant:
$\begin{vmatrix}67&19&21\\39&13&14\\81&24&26 \end{vmatrix}$

Write the inverse of 5 under multiplication modulo $11$ on the set ${1, 2, ... ,10}.$

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then write the values of $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$.

Represent the following families of curves by forming the corresponding differential equation:
$\text{x}^2+\text{y}^2=\text{a}^2$

Write the, negations of the following statements:
(a) $\forall n \in N , n+7>6$
(b) The kitchen is neat and tidy