Prove that cot x cot2x - cot2x cot3x - cot3x cotx = 1 - Vidyadip

Question

Prove that cot x cot2x - cot2x cot3x - cot3x cotx = 1

✓

Answer

We have cot 3x = cot (2x + x)
$ = \frac{{\cot 2x\cot x - 1}}{{\cot 2x + \cot x}}$
$\therefore $ cot 3x (cot 2x + cot x ) = cot 2x.cot x - 1
$ \Rightarrow \cot 3x \cdot \cot 2x$+ cot 3x.cot x = cot 2x.cot x - 1
$ \Rightarrow $ cot 3x cot 2x + cot 3x cot x - cot 2x cot x +1 = 0
$\therefore \cot x\cot 2x - \cot 2x\cot 3x$$ - \cot 3x \cdot \cot x = 1$

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 "1 Marks Question" 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

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2,11)}. Is the following given statement true? f is a relation from A to B. Justify your answer.

If U = {a, b, c, d, e, f, g, h}, find the complement of the set: B = {d, e, f, g}

Which of the following statements are true and which are false? In each case give a valid reason for saying so.
s: If x and y are integers such that x > y, then –x < – y.

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2,4, 6, 8} and C = {3, 4, 5, 6}. Find: $(A \cup B)'$

A coin is tossed 3 times and the out comes are recorded. How many possible outcomes are there?

Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.

Identify the Quantifiers in the following statement:
There exists a real number which is not a rational number.

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: B - A

Given an example of a statement P(n) such that it is true for all $\text{n}\in\text{N}.$

Answer each of the following questions in one word or sentence or as per exact requirement of the question
write the eccentricity of the hyperbola $9\text{x}^{2}-16\text{y}^{2}=144$