Cotx cot2x cot2x cot3x cot3x cotx 1

Cotx cot2x-cot2x cot3x-cot3x cotx=1 Formula

Prove that Cot X Cot 2x – Cot 2x Cot 3x – Cot 3x Cot X = 1 : In Trigonometry, we can easily find the relation between the angles and perpendicular, hypotenuse, base all sides of a triangle. The main concept behind Cotx cot2x cot2x cot3x cot3x cotx 1 is trigonometric Functions of Sum and Difference of Two Angles of sides of a triangle.

Prove that cot x. cot 2x – cot 2x. cot3x – cot x. cot3x = 1

To prove this trigonometric formula Cotx cot2x cot2x cot3x cot3x cotx 1, we have to use the trigonometric function of (cot (A+B) = ((cot A. cot B -1)/ (cot A + cot B)).

• Consider LHS of cot x. cot 2x – cot 2x. cot3x – cot x. cot3x = 1
• cot x. cot 2x – cot 2x. cot3x – cot x. cot3x
• cot x. cot 2x- cot 3x . (cot 2x+cot x) ——-> equation (1)
• 2x + x = 3x take both sides, cot so it will become cot(x + 2x) = cot3x

Using the Trigonometric 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))  Now we can put this value of cot(2x + x) or value of cot3x into equation 1.

• So now equation (1) becomes 
• cot x. cot 2x- cot2x.cotx–1cot2x+cotxcot2x.cotx–1cot2x+cotx . (cot 2x+cot x)
• = cot x. cot 2x- cot 2x. cot x – 1
• = 1 Which is equal to RHS

So LHS = RHS Hence proved. cot x. cot 2x – cot 2x. cot3x – cot x. cot3x = 1

How do you solve 1/cotx formula

Prove that 1 / cot x = tan x. We know that trigonometric ratio cot θ is equal to adjacent / opposite and cot a = cos a /sin a. Using these trigonometric ratios we can easily prove 1 / cot x = tan x formula.

• 1 / cot x can be expressed in terms of sin and cos as 1 / cot x = 1/ (cos x / sin x)
• 1 / cot x = sin x / cos x

We know that trigonometric ratio sin x / cos x is equal to tan x

So 1 / cot x = (sin x / cos x) and we know that sinx/cosx is equal to tanx. After substituting the values we will get 1 / cot x = tan x.

So 1 / cot x = tan x Hence proved. Please follow this link of Explanation of Mathematics formula – Click