Express sin3A and cos2A in terms of sine function

Let y=tan ^(-1)((1-cos x)/(sin x)) i) Express 1-cos x and sinx in terms of sin (x/2) and cos (x/2) ii) Hence find (dy/dx) .

Express sinA+sin3A and cosA+cos3A in product form

Discuss the continuity of sine function.

i) In which range is the inverse of sine defined? ii) What is the range for the inverse of cosine function? iii) Evaluate cos [sin ^(-1)((-4)/5)]

Express (8 cos^2 x + 11 sin x)/(cos x) as the sum of function and hence differentiate it w.r.t.x

Sajan finds the derivate of two functions f(x) = x^2 + cos x and g(x) = x^2 cos x as follows f(x) = x^2 + cos x , f'(x) = 2x - sin x, g (x) = x^2 cos x , g'(x) = 2x ( - sin x) Sajan makes a mistake in finding derivative of one of the functions. Identify that function and find out correct derivate of that function

Consider the trigonometric expression sin (2A)/(1-cos 2A) and sin(2A)/(1+cos 2A) . Of the above expressions which one is tan A and which one is cot A?

If sin A + cos 2A = 1/2 and cos A +sin 2A =1/3 , then find the value of sin 3A .

Consider the trigonometric expression sin(2A)/(1-cos 2A) amd sin(2A)/(1+cos 2A) .(iii)Prove that (1-cos theta)/sin theta=tan (theta/2)=(sin theta)/(1+cos theta) .