Problems from previous years' IIT Joint Entrance Examination (Indian Institute of Technology)

1. A circle is inscribed in an equilateral triangle of side 'a'. Find the area of the square inscribed in this circle.

2. Find the general value of  θ satisfying the equation
tan²θ+sec2 θ=1.

3. Solve the equation
sinx-3sin2x+sin3x = cosx-3cos2x+cos3x

4. Find all the solutions of
4cos²xsinx - 2sin²x = 3sinx.

5.If the expression