Find the general solution for each of the following equations: ^2… - Vidyadip

Question

Find the general solution for each of the following equations:
$\sec^22\text{x}=1-\tan2\text{x}$

✓

Answer

$\sec^22\text{x}=1-\tan2\text{x}$$\Rightarrow1+\tan^22\text{x}=1-\tan2\text{x}$
$\Rightarrow\tan^22\text{x}+\tan2\text{x}=0$
$\Rightarrow\tan2\text{x}(\tan2\text{x}+1)=0$
$\Rightarrow\tan2\text{x}=0$ or $\tan2\text{x}+1=0$
Now, $\tan2\text{x}=0$
$\Rightarrow\tan2\text{x}=\tan0$
$\Rightarrow2\text{x}=\text{n}\pi+0,$ where $\text{n}\in\text{Z}$
$\Rightarrow\text{x}=\frac{\text{n}\pi}{2},$ where $\text{n}\in\text{Z}$
$\tan2\text{x}+1=0$
$\Rightarrow\tan2\text{x}=-1=-\tan\frac{\pi}{4}=\tan\Big(\pi-\frac{\pi}{4}\Big)=\tan\frac{3\pi}{4}$
$\Rightarrow2\text{x}=\text{n}\pi+\frac{3\pi}{8},$ where $\text{n}\in\text{Z}$
$\Rightarrow2\text{x}=\frac{\text{n}\pi}{2}+\frac{3\pi}{8}$ where $\text{n}\in\text{Z}$
Therefore, the general solution is $\frac{\text{n}\pi}{2}$ or $\frac{\text{n}\pi}{2}+\frac{3\pi}{8},\text{n}\in\text{Z}$

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 "5 Marks Questions" from Trigonometric Functions→Trigonometric Functions — 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 three numbers in $GP,$ whose sum is $52$ and sum of whose product in pairs is $624.$

Represent to solution set of each of the following inequations graphically in two dimensional plane:
$-3\text{x}+2\text{y}\leq6$

$\text{If}\ \cos(\text{A+B})\sin(\text{C}-\text{D})=\cos(\text{A}-\text{B})\sin(\text{C+D}),$
prove that $\tan\text{A}\tan\text{B}\tan\text{C}+\tan\text{D}=0$

If $\frac2{11}$ is the probability of an event A, what is the probability of the event 'not A'.

Find the sum of the following geometric series:$(\text{x}+\text{y})+(\text{x}^2+\text{xy}+\text{y}^2)+(\text{x}^3+\text{x}^2\text{y}+\text{xy}^2+\text{y})+\ ...\text{ to n terms;}$

Find the mean deviation from the mean for following data:

$x_i$	$5$	$7$	$9$	$10$	$12$	$15$
$f_i$	$8$	$6$	$2$	$2$	$2$	$6$

Sketch the graphs of the following curves on the same scale and the same axes:
$\text{y}=\cos\text{x}$ and $\text{y}=\cos\frac{\text{x}}{2}$

Prove that $1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{\text{n}^2}<2-\frac{1}{\text{n}}$ for all $\text{n}>2,$ $\text{n}\in\text{N}.$

A manufacturer of radio sets produced $600$ units in the third year and $700$ units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find:

The production in the first year.
The total product in $7$ years and
The product in the $10^{th}$ year.

The probability of a person being alive in next $25$ years is $3 / 5$ and of his wife to be alive in same $25$ years is $2 / 3$. Calculate the probability of :
(1) both being alive,
(2) none being alive,
(3) at least one to be alive,
(4) only wife to be alive.