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
3. Solve the equation
sinx-3sin2x+sin3x = cosx-3cos2x+cos3x
4. Find all the solutions of
4cos²xsinx - 2sin²x = 3sinx.
5.If the expression
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