(nx)/(cos x)^(2))quad quad quad (x)(1)/(1+cot x)

Let P(x) = ((1- cos 2 x + sin 2x)/(1+ cos2x + sin2x))^(2) + ((1+ cot x + cot^(2) x)/( 1+ tan x+ tan^(2) x) ) , then the minimum value of P(x) equals

cos x + cos2x + ... + cos nx = sin ((nx) / (2)) cos ec ((x) / (2)) cos (((n + 1) x) / (2))

Prove that (cos x)/(1+sin x)=(cot ((x)/(2))-1)/(cot((x)/(2))+1)

1.lim_(x rarr0)(cos2x-1)/(cos x-1)(2).lim_(x rarr0)(1-cos2mx)/(1-cos2nx)

1- (sin ^ (2) x) / (1 + cot x) - (cos ^ (2) x) / (1 + tan x) = sin x cos x

1- (sin ^ (2) x) / (1 + cot x) + (cos ^ (2) x) / (1 + tan x) = sin x cos x

If y= (sin^(2)x)/(1+cot x)+ (cos^(2)x)/(1+tan x) , then y'(x) is equal to

(tan x)/(1-cot x)-(cot x)/(1-tan x)=(sec x cos(x+1))

f(x)=cos(x)/(2)+cot(x)/(4)+cos(x)/(8)+cot(x)/(16)+...+cos(x)/(2^(2n-1))+cot(x)/(2^(2n))

Let P(x)=cot^(2)x ((1+tanx+tan^(2)x)/(1+cot x+ cot^(2)x))+((cos x-cos 3x+sin3x-sin x)/(2(sin 2x+cos2x)))^(2) . Then, which of the following is (are) correct ?