Show that the following funtion are everywhere continuous ,
(i) sin x+ cos x (ii) `sin ^2x `
(iii) `|cos x|`

(1 + sin 2x + cos 2x )/( cos x + sin x ) = 2 cos x

Discuss the continuity of the following functions: (a) f(x) = sin x + cos x (b) f(x) = sin x - cos x (c) f(x) = sin x . cos x

Evaluate the following integrals. int sin x cos x (sin 2x + cos 2x) dx

Solve the following integration int (cos x - sin x)/(cos x + sin x)*(2+2 sin 2x)dx

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

Evaluate the following integrals int (cos^(2)x sin x)/(sin x - cos x)dx

Solve the following equations: (i) sin^(8)x - cos^(8)x=1 (ii) sin^(10)x - cot^(8)x=1

(i) int sin 2x. cos5x dx " "(ii) int(sin 4x)/(sin x) dx

Prove that: (sin 3 x +sin x) sin x + (cos 3x - cos x) cos x = 0

Find the derivative of the following functions. (i) (x^(2) tan x) (ii) (x + cos x) (sqrt(x) + 1) (iii) x^(-3) (e^(x) + 5 "sin" x)