" 6.(i) "4cot x-(1)/(2)cos x+(2)/(cos x)-(3)/(sin x)+(6cot x)/(cosec x)+9

(i) 4 cot x - 1/2 cos x + 2/cosx - 3/sin x + ( 6 cot x)/(cosecx) + 9 (ii) -5 tan x + 4 tan x cos x -3 cotx sec x + 2 sec x -13

(cosec x-sin x)(sec x-cos x)(tan x+cot x)

For 0 lt x lt (pi)/(2),(sin x )/(cos x )*( sec x)/("cosec" x)*( tan x)/(cot x )=9 . Then x=

(sin 2x)/(1- cos 2x ) = cot x

(cosec x-sin x)(sec x-cos x)(tan x+cot x)=1

cosec x(sec x-1)-cot x(1-cos x)=tan x-sin x

cosec x(sec x-1)-cot x(1-cos x)=tan x-sin x

Evaluate: (i) int(1-cos x)/(1+cos x)dx (ii) int{3sin x-4cos x+(5)/(cos^(2)x)-(6)/(sin^(2)x)+tan^(2)x-cot^(2)x}dx

Prove that (1+ cos x)/(1-cos x) = "(cosec x + cot x)^(2)

Find the derivative of the following functions: (i) sin x cos x (ii) sec x (iii) 5sec x+4 cos x (iv) cosec x (v) 3 cot x+5 cosec x (vi) 5sinx-6cosx+7 (vii) 2tanx-7secx