" (xxiii) "sin x+cos x=(1)/(sqrt(2))

If "sin" x + "sin"^(2) x = 1 show that: cos^(4)x + cos^(2)x = 1 (ii) If "sin" x + cos x =sqrt(2) cos x show that: sqrt2 sin x = cos x - sin x

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

sin x + cos x = sqrt (2) cos A

The value of int(sin x+cos x)/(sqrt(1-sin2x))dx is equal to sqrt(sin2x)+C(b)sqrt(cos2x)+C(c)+-sin x-cos x)+C(d)+-log(sin x-cos x)+C

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0

sin^(-1)x=cos^(-1)sqrt(1-x^(2))

If tanx=b/a then sqrt((a+b)/(a-b))+sqrt((a-b)/(a+b))= ........................... A) (2 sin x)/(sqrt(sin2x)) B) (2 cos x)/(sqrt(cos2x)) C) (2 cos x)/(sqrt(sin2x)) D) (2 sin x)/(sqrt(cos2x))

int(sin^(3)x cos x)/(sqrt(a-sin^(2)x)sqrt(a+sin^(2)x))backslash dx=

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

If x , y in R , then the determinant = |(cos x , -sin x,1),(sin x, cos x,1),(cos(x+y), -sin(x+y), 0)| lies in the interval (a) [-sqrt(2),sqrt(2)] (b) [-1,1] (c) [-sqrt(2),1] (d) [-1,-sqrt(2)]