" (b) "cos A=(1-tan^(2)(A)/(2))/(1+tan^(2)(A)/(2))

If A=30^(@) , verify that (i) sin2A=(2tanA)/(1+tan^(2)A) (ii) cos2A=(1-tan^(2)A)/(1+tan^(2)A) (iii) tan2A=(2tanA)/(1-tan^(2)A)

cos ^ (2) A-sin ^ (2) A = (1-tan ^ (2) A) / (1 + tan ^ (2) A)

Prove that cos2A=(1-tan^2 A)/(1+tan^2 A)

If A= 30^@ verify that :- cos2A= (1-tan^2A)/(1+tan^2A) .

Prove that: tan(A+B)tan(A-B)=(tan^(2)A-tan^(2)B)/(1-tan^(2)A tan^(2)B)

Prove that: (tan(A+B))/(cot(A-B))=(tan^(2)A-tan^(2)B)/(1-tan^(2)A tan^(2)B)

Prove that tan((pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)) +tan((pi)/(4) -(1)/(2) "cos"^(-1)(a)/(b)) =(2b)/(a) .

cos ^(-1) ""((cos x + cos y)/(1+cos x cos y))= 2 tan ^(-1) (tan ""(x)/(2) tan ""(y)/(2))

cos ^(-1) ((3+5 cos x )/(5+3 cos x )) is equal to : a) tan ^(-1) ((1)/(2) tan ""(x)/(2)) b) 2 tan ^(-1) (2 tan ""(x)/(2)) c) (1)/(2) tan ^(-1) (2 tan ""(x)/(2)) d) 2 tan ^(-1) ((1)/(2) tan ""(x)/(2))

prove that tan ((pi) / (4) + (1) / (2) cos ^ (- 1) ((a) / (b))) + tan ((pi) / (4) - (1) / (2) cos ^ (- 1) ((a) / (b))) = (b) / (a) cos ^ (- 1) ((cos x + cos y) / (1 + cos x cos y) ) = 2tan ^ (- 1) ((tan x) / (2) (tan y) / (2))