" 37."tan^(-1)((1)/(2)sec x)+cot^(-1)(2cos x)=(pi)/(3)

tan ^(-1) (cot x) + cot ^(-1) (tan x) =(pi)/(4)

tan^(-1)((2x)/(1-x^2))+cot^(-1)((1-x^2)/(2x))=pi/3

tan^(-1) (cot x) +cot^(-1)(tan x) =pi -2x

prove that tan^(-1)((cos x)/(1-sin x))-cot^(-1)((sqrt(1+cos x))/(sqrt(1-cos x)))=(pi)/(4),x varepsilon(0,(pi)/(2))

y = tan ^ (- 1) (cot x) + cot ^ (- 1) (tan x), (pi) / (2)

tan^(3)x-1+(1)/(cos^(2)x)-3cot((pi)/(2)-x)=3

The solution set of inequality (tan^(-1)x)(cot^(-1)x)-(tan^(-1)x)(1+(pi)/(2))-2cot^(-1)x+2(1+(pi)/(2))gtlim_(yrarr-oo)[sec^(-1)y-(pi)/(2)] is (where [ . ]denotes the G.I.F.)

The solution set of inequality (tan^(-1)x)(cot^(-1)x)-(tan^(-1)x)(1+(x)/(2))-2cot^(-1)x+2(1+(pi)/(2))gtlim_(yrarr-oo)[sec^(-1)y-(pi)/(2)] is (where [ . ]denotes the G.I.F.)

The solution set of inequality (tan^(-1)x)(cot^(-1)x)-(tan^(-1)x)(1+(x)/(2))-2cot^(-1)x+2(1+(pi)/(2))gtlim_(yrarr-oo)[sec^(-1)y-(pi)/(2)] is (where [ . ]denotes the G.I.F.)