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 "3 Marks Question" from Trigonometric Equations→Trigonometric Equations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the point of intersection of the following pairs of lines:
bx + ay = ab and ax + by = ab.

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\infty}}{\sqrt{\text{x}+1}-\sqrt{\text{x}}}{}$

If $\text{f(x)}=\log_\text{e}(1-\text{x})$ and $\text{g(x)}=[\text{x}],$ then determine the following functions:
(fg)(0)

Differentiate the following function with respect to x:$(1-2\tan\text{x})(5+4\sin\text{x})$

In a race, the odds in favour of horses A, B, C, D are 1 : 3, 1 : 4, 1 : 5 and 1 : 6 respectively. Find probability that one of them wins the race.

If $\tan\text{A}=\frac{\text{a}}{\text{a}+1}$ and $\text{B}=\frac{1}{2\text{a}+1},$ then the value of $A + B$ is:

How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?

Show the following quadratic equation by factorization method:
$17x^2 - 28x + 12 = 0$

Find the mean deviation about the median for the data in: $13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17.$

Evaluate the following:
$(\sqrt3+1)^5-(\sqrt3-1)^5$