[" wing cases: "],[qquad " (ii) "y=(x+cos x)/(tan x)]

" (ii) "(sin y)^(x)=(cos x)^(y)

Find the derivative of (i)(x^(5)-cos x)/(sin x) (ii) (x+cos x)/(tan x)

Evaluate: (i) int(tan x)/(sec x+tan x)dx (ii) int(cos ecx)/(cos ec)x-cot x

Prove the following: (i) ("sin" x+"sin" y)/(cos x+cos y)="tan""(x+y)/(2) (ii) (cos 7x+cos 5x)/("sin" 7x-"sin" 5x)=cot x .

Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the case: tan x = (-4)/(3) , x in II quadrant.

Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the case: sin x = (1)/(4), x in II quadrant.

If (cos x)^y = (cos y)^x then show that (dy)/(dx) = (y tan x+log cos y)/(x tan y+log cos x).

If tan A=(x sin B)/(1-cos B)tan B=(y sin A)/(1-y cos A) then (x)/(y)=

Evaluate: (i) int(1+tan x)/(1-tan x)dx (ii) int(cos x)/(cos(x-a))dx

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