[" Prove each of the following: "],[" (a) "quad sin^(-1)(1)/(sqrt(5))+sin^(-1)(2)/(sqrt(5))=(pi)/(2)]

Prove each of the following sin^(- 1)(3/5)+sin^(- 1)(8/17)=sin^(- 1)(77/85)

Prove each of the following sin^(- 1)(3/5)+sin^(- 1)(8/17)=sin^(- 1)(77/85)

Prove each of the following sin^(-1)((3)/(5))+sin^(-1)((8)/(17))=sin^(-1)((77)/(85))

Prove each of the following sin^(-1)((3)/(5))+sin^(-1)((8)/(17))=sin^(-1)((77)/(85))

Prove each of the following tan^(-1) x=-pi +cot^(-1) 1/x=sin^(-1) (x)/(sqrt(1+x^(2)) =-cos^(-1) (1)/(sqrt(1+x^(2))" when "x lt 0

Prove each of the following tan^(-1) x=-pi +cot^(-1) 1/x=sin^(-1) (x)/(sqrt(1+x^(2)) =-cos^(-1) (1)/(sqrt(1+x^(2))" when "x lt 0

Prove each of the following identities : (i) cot^(2) theta - (1)/(sin^(2) theta)=-1 " " (ii) tan^(2) theta - (1)/(cos^(2) theta)=-1 (iii) cos^(2) theta + (1)/((1+ cot^(2) theta))=1

Using the principle of mathmatical induction, prove each of the following for all n in N 1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)(2n+1))=n/((2n+1))

Prove each of the following identities : (i) (sec theta -1)/(sec theta +1) =(sin^(2) theta)/((1+ cos theta)^(2) ) (ii) (sec theta - tan theta)/(sec theta + tan theta) = (cos^(2) theta)/((1+ sintheta)^(2))