Prove that `4(cot^(- 1)3+c o s e c^(- 1)sqrt(5))=pi`

Prove that cot^(-1) 9 + cosec^(-1) sqrt(41)/4 = pi/4

Prove that: sec(tan^-1 1)+cos e c(cot^(-1) 1)=4

Prove that cot(pi/4-2cot^(- 1)3)=7

Prove that cot(pi/4-2cot^(- 1)3)=7

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

Find the principal values of " (1) c o s e c"^(-1)(2) and "c o s e c"^(-1)(-2/(sqrt(3)))

For the principal values, evaluate the following: (1) cot^(-1)(-1)+cos e c^(-1)(-sqrt(2))+s e c ^(-1)(2) (2) cot^(-1)(-sqrt(3))+tan^(-1)(1)+sec^(-1)(2/(sqrt(3)))

Prove that: cos e c(tan^(-1)("cos"(cot^(-1)("sec"(sin^(-1)a)))))=sqrt(3-a^2), where a in [0,1]

Prove that: cos e c(tan^(-1)("cos"(cot^(-1)("sec"(sin^(-1)a)))))=sqrt(3-a^2), where a in [0,1]