(1/2) tan ((x/2))+ (1/4) ( tan (x/4)) + ... + (1/2n) tan((x/2n)) =

Question

(1/2) tan ((x/2))+ (1/4) ( tan (x/4)) + ... + (1/2n) tan((x/2n)) =  (A) (1/2n) cot ( (x/2n) ) (B) (1/2n) cot ( (x/2n) ) + cot x  (C) (1/2n) cot ( (x/2n) ) - cot x  (D)  cot ( (x/2n) ) - cot x

Tardigrade Admin · Accepted Answer

Put n = 1 and verify the options.

Q. $\frac{1}{2} tan (\frac{x}{2}) + \frac{1}{4} (tan \frac{x}{4}) + ... + \frac{1}{2 ^{n}} tan (\frac{x}{2 ^{n}}) =$

$\frac{1}{2 ^{n}} cot (\frac{x}{2 ^{n}})$

$\frac{1}{2 ^{n}} cot (\frac{x}{2 ^{n}}) + cot x$

$\frac{1}{2 ^{n}} cot (\frac{x}{2 ^{n}}) - cot x$

$cot (\frac{x}{2 ^{n}}) - cot x$

Put n = 1 and verify the options.

Q. 21​tan(2x​)+41​(tan4x​)+...+2n1​tan(2nx​)=

2n1​cot(2nx​)

2n1​cot(2nx​)+cotx

2n1​cot(2nx​)−cotx

cot(2nx​)−cotx

Put n = 1 and verify the options.

Q. $\frac{1}{2} tan (\frac{x}{2}) + \frac{1}{4} (tan \frac{x}{4}) + ... + \frac{1}{2 ^{n}} tan (\frac{x}{2 ^{n}}) =$

$\frac{1}{2 ^{n}} cot (\frac{x}{2 ^{n}})$

$\frac{1}{2 ^{n}} cot (\frac{x}{2 ^{n}}) + cot x$

$\frac{1}{2 ^{n}} cot (\frac{x}{2 ^{n}}) - cot x$

$cot (\frac{x}{2 ^{n}}) - cot x$