Solve the following equations: + =2 - Vidyadip

Question

Solve the following equations:
$\cot\text{x}+\tan\text{x}=2$

✓

Answer

$\cot\text{x}+\tan\text{x}=2$
$\Rightarrow\frac{1}{\tan\text{x}}+\tan\text{x}=2$
$\Rightarrow\tan^{2}\text{x}+1=2\tan\text{x}$
$\Rightarrow\tan^{2}\text{x}-2\tan\text{x}+1=0$
$\Rightarrow(\tan\text{x}-1)^{2}=0$
$\Rightarrow\tan\text{x}=1=\tan\frac{\pi}{4}$
$\Rightarrow\text{x}=\text{n}\pi+\frac{\pi}{4},\text{n}\in\text{Z}$ $(\tan\text{x}=\tan\alpha\Rightarrow\text{x}=\text{n}\pi+\alpha,\text{n}\in\text{z)}$

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.(4 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

Prove by the method of induction, for all n ∈ N.

$1^2+4^2+7^2+\ldots \ldots+(3 n-2)^2=\frac{n}{2}\left(6 n^2-3 n-1\right)$

If ${^\text{28}}\text{C}_{2\text{r}}:{^\text{24}}\text{C}_{\text{2r-4}},=225:11,$ Find r.

Prove that
$\cos\frac{2\pi}{15}\cos\frac{4\pi}{15}\cos\frac{8\pi}{15}\cos\frac{16\pi}{15}=\frac{1}{16}$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{{\pi}}}\frac{1+\cos\text{x}}{\tan^2\text{ x}}$

A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes in how many ways can the teams be constituted?

Find the total number of arrangements of the letters in the expression $a^3 b^2 c^4$ when written at full length.

Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{6}}\left[\frac{\cos x-\sqrt{3} \sin x}{\pi-6 x}\right]$

A box contains 10 red balls and 15 green balls. Two balls are drawn in succession without replacement. What is the probability that,

i. the first is red and the second is green?

ii. one is red and the other is green?

Find the area of quadrilateral whose vertices are A (- 3,1), B (- 2, – 2), C (1,4), D (3, – 1).

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\tan2\text{x}-\sin2\text{x}}{\text{x}^3}$