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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Prove that cot x. cot 2x - cot 2x. cot3x - cot x. cot3x = 1.
Trigonometry is a branch of mathematics that deals with the relation between the angles and sides of a triangle.
Answer: cot x. cot 2x - cot 2x. cot3x - cot x. cot3x = 1
We will use the trigonometric formula (cot (A+B) = ((cot A. cot B -1)/ (cot A + cot B))
Explanation:
Consider LHS:
cot x. cot 2x - cot 2x. cot3x - cot x. cot3x
cot x. cot 2x- cot 3x . (cot 2x+cot x) -------> (1)
cot 3x = cot (2x+x)
Using the formula,
cot (A+B) = ((cot A. cot B -1)/ (cot A + cot B)
We have,
cot (2x+x) = ((cot 2x. cot x – 1) / (cot 2x + cot x))
(1) becomes
cot x. cot 2x- \(\dfrac{cot 2x. cot x – 1}{cot 2x + cot x}\) . (cot 2x+cot x)
= cot x. cot 2x- cot 2x. cot x – 1
= 1 = RHS
⇒ cot x. cot 2x - cot 2x. cot3x - cot x. cot3x = 1.
Hence, proved cot x. cot 2x - cot 2x. cot3x - cot x. cot3x = 1.
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