1.$ cotx - tanx + 4sin2x = \frac{2}{sin2x} $2.$ cos^{4} + sin^{4} + cos(x-\frac{\pi }{4}).sin(3x-\frac{\pi }{4}) - \frac{3}{2} $3.$ \frac{(1+ sinx+cos2x).sin(x+\frac{\pi }{4})}{1+tanx} = \frac{1}{\sqrt{2}}cosx $4.$ \frac{(1-2sinx)cosx}{(1+2sinx).(1-sinx)} = \sqrt{3} $5.$ sin^{3}x-\sqrt{3}cos^{2}x=sinx.cos^{2}x-\sqrt{3}sin^{2}x.cosx $...