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Question

Is sin2x the same as 2sinx?


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Solution

Identifying is sin2x is the same as 2sinx:

sin2x is not the same as 2sinx.

Sine of twice of an angle (x) is equal to twice of sinxcosx.

By trigonometric identities,

sin2x=2sinxcosx...(1)

where xis a reference angle in a right-angled triangle

Therefore,

2sinx=sin2xcosx...(2)

Hence, we can see from the above equation that 2sinx is not equal to 2sinx.

We can also prove it by an example;

Suppose, ifx=Ï€2, then,

sin2x=sin2(π2)=sinπ=0...(3)

Now,

2sinx=2sin(π2)=2(1)=2...(4)[∵sinπ2=1]

From equations 3and4, we get;

sin2x≠2sinx

Hence, it is evident that sin2x is not the same as 2sinx.


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