Prove that (`tan^(-1)` `1/e)^2`+`(2e)`/`root e^2+1`<(tan^(-1)e)^2+2/(sqrt(e^2+1))`

Prove that (tan^(-1)(1/e))^(2)+(2e)/(sqrt(e^(2)+1) lt (tan^(-1) e)^2 + (2)/(sqrt(e^(2)+1)

Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(sec^(-1)2)+cot^2(cos e c^(-1)3)=11

Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(sec^(-1)2)+cot^2(cos e c^(-1)3)=11

Prove that 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x)=tan^(-1)x(x!=0)dot

Prove that: ((1+tan^2theta)cottheta)/(c o s e c^2theta)=tantheta

Prove that 1 le int_(0)^(1) e^(x^(2))dxle e

The value of int_1^e((tan^(-1)x)/x+(logx)/(1+x^2))dx ,is (a) tane (b) tan^(-1)e (c) tan^(-1)(1/e) (d) none of these

The value of int_1^e((tan^(-1)x)/x+(logx)/(1+x^2))dxi s tane (b) tan^(-1)e tan^(-1)(1/e) (d) none of these

If the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1and(y^(2))/(b^(2))-(x^(2))/(a^(2))=1" are "e_(1)ande_(2) respectively then prove that : (1)/(e_(1)^(2))+(1)/(e_(2)^(2))=1

Prove that: (alpha^3)/2cos e c^2(1/2tan^(-1)(alpha/beta))+(beta^3)/2s e c^2(1/2tan^(-1)(beta/alpha))=(alpha+beta)(alpha^2+beta^2) .