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 "(Each question 4 marks)" from Trigonometric Equations→Trigonometric Equations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\sin^3\text{x}+\sin^3\big(\frac{2\pi}{3}+\text{x}\big)+\sin^3\big(\frac{4\pi}{3}+\text{x}\big)=-\frac{3}{4}\sin3\text{x}$

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that:
$\text{A}\times\text{C}\subset\text{B}\times\text{D}$

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): $\frac{\sin\text{x}+\cos\text{x}}{\sin\text{x}-\cos\text{x}}$

Prove that the area of the parallelogram formed by the lines 3x - 4y + a = 0, 3x - 4y + 3a= 0, 4x - 3y - a = 0 and 4x - 3y - 2a = 0 is $\frac{2\text{a}^2}{7}$ sq.units.

If then $\text{x}+\tan\Big(\frac{\pi}{3}\Big)+\tan\Big(\text{x}=\frac{2\pi}{3}\Big)=3,$prove that $\frac{3\tan\text{x}-\tan^3\text{x}}{1-3\tan^2\text{x}}=1$

Prove that: $\frac{\sin\text{A}+\sin3\text{A}+\sin5\text{A}}{\cos\text{A}+\cos3\text{A}+\cos5\text{A}}=\tan3\text{A}$

Evaluate $^{20}\text{C}_{5}+\sum\limits_\text{r=2}^5\ ^{25-\text{x}}\text{C}_4.$

Let r and n be positive integers such that 1 < r < n. Then prove the following: $\frac{{{^\text{n}}\text{C}_{\text{r}}}}{{^\text{n-1}}\text{C}_{\text{r}-1}}=\frac{\text{n}}{\text{r}}$

If $\text{x}-\text{iy}=\sqrt{\frac{\text{a}-\text{ib}}{\text{c}-\text{id}}}$ Prove that $(\text{x}^2+\text{y}^2)^2=\frac{\text{a}^2+\text{b}^2}{\text{c}^2+\text{d}^2}.$

Find the equations of the medians of a triangle, the equations of whose sides are: 3x + 2y + 6 = 0, 2x - 5y + 4 = 0 and x - 3y - 6 = 0