[" 40.(a) "log(sec x)],[" (b) "sqrt(x sin x)]

The smallest positive value of x (in radians ) satisfying the equation log_(cos x) ((sqrt(3))/(2) sin x) = 2 + log _(sec x) tan x)

(i)tan (logx)" "(ii)log sec x" "(iii) log sin.(x)/(2)

The value of int _(sqrt ( log 2 )) ^(sqrt( log 3 )) (x sin x ^(2))/( sin x ^(2) + sin (log 6 -x ^(2)))dx is

(i) int (1+ tan x)/(x +log sec x) dx (ii) int (1+ cot x)/(x+log sin x) dx.

Evaluate: (i) int(1+tan x)/(x+log sec x)dx (ii) int(sin2x)/(a^(2)+b^(2)sin^(2)x)dx

(d)/(dx)(log tan((pi)/(4)+(x)/(2)))= (a) cosec x (b) -cosec x (c) sec x (d) -sec x

If I=int(sqrt(cot x)-sqrt(tan x))dx, then I equal sqrt(2)log(sqrt(tan x)-sqrt(cot x))+Csqrt(2)log|sin x|cos x+sqrt(sin2x)|+Csqrt(2)log|sin x-cos x+sqrt(2)sin x cos x|+sqrt(2)log|sin(x+(pi)/(4))+sqrt(2)sin x cos x|+C

Find (dy)/(dx)(1)sqrt(log x)(2)sqrt(sec x)(3)sqrt(log_(a)x)

If y=(sin x)^(tan x), then (dy)/(dx)= (a) (sin x)^(tan x)(1+sec^(2)x log sin x)(b)tan x(sin x)^(tan x-1)cos x(c)(sin x)^(tan x)(d)sec^(2)x log sin x tan x(sin x)^(tan x-1)