" 7."x cot^(2)x

int7x cot^(2)xdx

All x satisfying the inequality (cot^(-1) x)^(2) - 7 (cot^(-1) x) + 10 gt0 lie in the interval

All x satisfying the inequnality (cot^(-1) x)^(2) - 7 (cot^(-1) x) + 10 gt0 lie in the inteval

f(x)=cot^(2)x*cos^(2)x, g(x)=cot^(2)x-cos^(2)x

f(x)=cot^(2)x*cos^(2)x, g(x)=cot^(2)x-cos^(2)x

Prove that, cot x cos^(2)x -tan x sin^(2)x = 2 cot 2x

cot x cos^(2)x-tan x sin^(2)x=2cot2x

int (x+ cot x)cot^(2) x dx

Statement-1: cosec^(-1)(3)/(2)+cos^(-1)(2/3)-2cot^(-1)(1/7)-cot^(-1)7=cot^(-1)7 Statement-2: cos^(-1)x=sin^(-1)((1)/(x)) and for xgt0cot^(-1)x=tan^(-1)((1)/(x))

Statement-1: cosec^(-1)(3)/(2)+cos^(-1)(2/3)-2cot^(-1)(1/7)-cot^(-1)7=cot^(-1)7 Statement-2: cos^(-1)x=sin^(-1)((1)/(x)) and for xgt0cot^(-1)x=tan^(-1)((1)/(x))