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| 1. |
Prove that sin theeta - 2sin^3 theeta /2cos^3 theeta -cos theeta is equal to tan theeta |
| Answer» LHS = (sin{tex}\\theta{/tex}\xa0- 2sin3{tex}\\theta{/tex})= sin{tex}\\theta{/tex}(1 - 2sin2{tex}\\theta{/tex})RHS = (2cos3{tex}\\theta{/tex}\xa0- cos{tex}\\theta{/tex})tan{tex}\\theta{/tex}= cos{tex}\\theta{/tex}(2cos2{tex}\\theta{/tex}\xa0- 1){tex}\\frac { \\sin \\theta } { \\cos \\theta }{/tex}= [2(1 - sin2{tex}\\theta{/tex}) - 1)sin{tex}\\theta{/tex}= (2 - 2sin2{tex}\\theta{/tex}\xa0-1)sin{tex}\\theta{/tex}= (1 - 2sin2{tex}\\theta{/tex})sin{tex}\\theta{/tex}{tex}\\Rightarrow{/tex}\xa0LHS = RHS{tex}\\therefore{/tex}\xa0(sin{tex}\\theta{/tex}\xa0- 2sin3{tex}\\theta{/tex}) = (2cos3{tex}\\theta{/tex}\xa0- cos{tex}\\theta{/tex})tan{tex}\\theta{/tex} | |