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Sin2x=2sinxcosx |
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Answer» We know,\xa0one important identity ,\xa0sin( A + B) =sinA.cosB + cosA. sinB\xa0let A = x\xa0B = x\xa0then,\xa0sin( x + x ) = sinx.cosx + cosx .sinx\xa0sin2x = 2sinx.cosx\xa0verify :-\xa0Let x = 30°\xa0LHS = sin60° = √3/2\xa0RHS = 2sin30°.cos30° = 2× 1/2 × √3/2 =√3/2\xa0LHS = RHS\xa0this is true for all real value of x then ,sin2x = 2sinx.cosx is also an identity. We knowsin(x+y)=sinxcosy+cosxsinyif x=y thensin(x+x)=sinxcosx+cosxsinxsin2x=2sinxcosx |
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