Find the general solutions of the following equations: = - Vidyadip

Question

Find the general solutions of the following equations:
$\tan\text{px}=\cot\text{qx}$

✓

Answer

We have,
$\tan\text{px}=\cot\text{qx}$
$\Rightarrow\tan\text{px}=\tan\Big(\frac{\pi}{2}-\text{qx}\Big)$
$\Rightarrow\text{px}=\text{nx}\pm\Big(\frac{\pi}{2}-\text{qx}\Big),\text{n}\in\text{z}$
$\Rightarrow\text{(p+q)}\text{x}=\text{n}\pi+\frac{\pi}{2},\text{n}\in\text{z}$
$\Rightarrow\text{(p+q)}\text{x}=\text{(2n+1)}\frac{\pi}{2},\text{n}\in\text{z}$
$\Rightarrow\text{x}=\frac{\text{(2n+1)}}{\text{(p+q)}}\frac{\pi}{2},\text{n}\in\text{z}$

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.(3 Marks)" from Trigonometric Equations→Trigonometric Equations — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Use the binomial theorem to evaluate the following upto four places of decimals.

$\sqrt[4]{16.08}$

Show that $\frac{n !}{r !(n-r) !}+\frac{n !}{(r-1) !(n-r+1) !}=\frac{(n+1) !}{r !(n-r+1) !}$

Two plants A and B of a factory show following results about the number of workers and the wages paid to them:

	Plant A	Plant B
No. of workers	5000	6000
Average monthly wages	₹ 2500	₹ 2500
Variance of distribution of wages	81	100

In which plant A or B is there greater variability in individual wages?

Prove that: $\cos^2\frac{\pi}{4}-\sin^2\frac{\pi}{12}=\frac{\sqrt{3}}{4}$

∆PQR is an equilateral triangle with side 18 cm. A circle is drawn on segment QR as diameter. Find the length of the arc of this circle within the triangle.

Classify the following pairs of lines as coincident, parallel or intersecting:
3x + 2y - 4 = 0 and 6x + 4y - 8 = 0.

In a group photograph, 6 teachers and principal are in the first row and 18 students are in the second row. There are 12 boys and 6 girls among the students. If the middle position is reserved for the principal and if no two girls are together, find the number of arrangements.

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow2^-}\frac{\text{x}-3}{\text{x}^2-4}.$

A ball is dropped from a height of 10 m. It bounces to a height of 6m, then 3.6 m, and so on. Find the total distance travelled by the ball.

Evaluate the following limits: $\lim _{\theta \rightarrow 0}\left[\frac{\sin (m \theta)}{\tan (n \theta)}\right]$