" 20."(sin(3-4x))/(cos^(2)(3-4x))

If f_(n)(x) = (sin x)/(cos3x)+(sin 3x)/(cos 3^(2)x) +(sin 3^(2)x)/(cos 3^(3)x) +....+ (sin 3^(n-1)x)/(cos 3^(n)x)"Then" f_(2) ((pi)/(4)) + f_(3) ((pi)/(4))=

(i) int_0^(pi//2) (sin^3x)/(sin^3x+cos^3x) dx (ii) int_0^(pi//2) (cos^3x)/(sin^3x+cos^3x) dx (iii) int_0^(pi//2) (sin^4x)/(sin^4x+cos^4x) dx (iv) int_0^(pi//2) (cos^5x)/(sin^5x+cos^5x) dx (v) int_0^(pi//2) (sin^5x)/(sin^5x+cos^5x) dx

int(4cos^(2)x-3sin^(2)x)/(sin^(2)2x)d(4x)=

int_(-1/2)^(1/2) [sin^(-1)(3x-4x^(3)) - cos^(-1) (4x^(3)-3x)] dx =

Prove that (cos(4x)+cos(3x)+cos(2x))/(sin(4x)+sin(3x)+sin(2x))=cot(3x)

(d^(20))/(dx^(20))(2cos x cos3x)=2^(20)(cos2x-2^(20)cos4x)(b)2^(20)(cos2x+2^(20)cos4x)(c)2^(20)(sin2x+2^(20)sin4x)(d)2^(20)(sin2x-2^(20)sin4x)

(sin2x-sin3x+sin4x)/(cos2x-co3x+cos4x)=

int(sin^3x+sin^5x)/(cos^2x+cos^4x)dx

int(sin^3x+sin^5x)/(cos^2x+cos^4x)dx