(" (iii) "sin^(5)x

Find the extreme values of the following function over R. (i) sin^(2) (60^(0) + x) + sin^(2) (60^(0) - x) (ii) cos (x+ (Pi)/(3) ) + 2sqrt(2) sin (x+ (pi)/(3))-3 (iii) 3 sin^(2) x+ 5 cos^(2) x (iv) cos 2 x+ cos^(2) x (v ) cos x cos ((2pi)/(3) + x) cos ((2pi)/(3)-x)

Sketch the graphs of the following function: (i) y=2 sin x (ii) y=3 "sin"(x+1) (iii) y="sin"(x)/(2)

Find the principal solutions of each of the following equations : (i) sinx=(-1)/(2) "sin "(3x)/(2)=0 (iii) sin(x+(pi)/(5))=0 (iv) cos2x=0 (v) "cos"(5x)/(2)=0 (vi) cos(x+(pi)/(10))=0

Find the derivative of the following functions using first principle of derivative. (i) sin (3x + 2) (ii) "sin" (x^(2) + 5) (iii) x cos x

Find the derivative of the following functions using first principle of derivative. (i) sin (3x + 2) (ii) "sin" (x^(2) + 5) (iii) x cos x

Differentiate the following : (iii) cos^(2)x sin x^(2)

Evaluate the integrals . int_(0)^(pi//2) (sin^(5)x)/(sin^(5)x + cos^(5)x)dx

Find int_(0)^(pi//2) (sin^(5)x)/(sin^(5)x + cos^(5)x)dx

Evaluate : int_(0)^( pi/2)(sin^(5)x)/(sin^(5)x+cos^(5)x)dx