" 2."(i)" tan "^(2)x

If tan x=(-4)/(3) " and " .(pi)/(2) lt x lt pi find the values of (i) " sin ".(x)/(2) " ""(ii) cos " .(x)/(2) " ""(iii) tan ".(x)/(2)

(d) / (dx) [((tan ^ (2) 2x-tan ^ (2) x) / (1-tan ^ (2) 2x tan ^ (2) x)) cot3x] =

If tan x=(-3)/(4) " and" (3pi)/(2) lt x lt 2 pi find the value of "(i) " sin 2x , "(ii) " cos 2x , "(iii) " tan 2x

(i) tan^(-1)sqrt(x) (ii) tan ^(-1)(2x+1)

(i) tan^(-1)sqrt(x) (ii) tan ^(-1)(2x+1)

Show that tan" "3x" "tan" "2x" "tan" "x" "=" "tan 3x - tan 2x - tan x .

If tan x=(3)/(4) " and " pi lt x lt .(3pi)/(2) find the value of (i) sin.(x)/(2) , (ii) cos .(x)/(2) , (iii) tan .(x)/(2)

Evaluate: (i) int tan^(3)x sec^(2)xdx (ii) int tan x sec^(4)xdx

If I_(n)=int tan^(n)xdx then I_(0)+I_(1)+2(I_(2)+......+I_(8))+I_(9)+I_(10)= (a) (tan x)/(1)+(tan^(2)x)/(2)+....+(tan^(9)x)/(9), (b) -((tan x)/(1)+(tan^(2)x)/(2)+......+(tan^(9)x)/(9)) (c) (cot x)/(1)+(cot^(2)x)/(2)+......+(cot^(9)x)/(9) (d) -((cot x)/(1)+(cot^(2)x)/(2)+......+(cot^(9)x)/(9))