[sqrt(ln)(tan x)/(tan y)=(1+cos^(2)x)/(1+sin^(2)x)>=3,sqrt(6)ch2log_(x)2],[sin(3x+y)=7sin(x-y)1]

If (tan x) / (tan y) = (1 + cos ^ (2) x) / (1 + sin ^ (2) x), show that sin (3x + y) = 7sin (xy)

If (tan x) / (tan y) = (1 + cos ^ (2) x) / (1 + sin ^ (2) x), show that sin (3x + y) = 7sin (xy)

"If " (tan x)/(tan y) = (1 + cos^(2) x)/(1 + sin^(2) x ) " show that "sin ( 3x + y) =7sin (x-y).

If y=log sqrt((1+sin^(2)x)/(1-sin^(2)x)), then find (dy)/(dx)

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)

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

int(sin2x)/(sin^(2)x+2cos^(2)x)dx(i)-log(1+sin^(2)x)+C(ii)log(1+cos^(2)x)+C( iii) -log(1+cos^(2)x)+C(iv)log(1+tan^(2)x)+C

int(sin2x)/(sin^(2)x+2cos^(2)x)dx(i)-log(1+sin^(2)x)+C(ii)log(1+cos^(2)x)+C( iii) -log(1+cos^(2)x)+C(iv)log(1+tan^(2)x)+C

int(2sin x)/((3+sin2x))dx is equal to (1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(2sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(4)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+cnone of these