If 0 x

Question

If 0 x< 2, then the number of values of x for which sinx- sin2x+ sin3x=0, is;

Accepted Answer

Correct answer: D. (d) JEE Main 2019 sinx- sin2x+ sin3x=0 ⇒ sinx-2 sinx . cosx+3 sinx-4 sin^3x=0 ⇒4 sinx-4 sin^3x-2 sinx . cosx=0 ⇒2 sinx(1- sin^2x)- sinx . cosx=0 ⇒2 sinx . cos^2x- sinx . cosx=0 ⇒ sinx . cosx(2 cosx-1)=0 ∴ sinx=0 , cosx=0 , cosx= 12 ∴x=0 , 3 ∵x ∈ (0 , 2 )

$If 0 \leq x < \frac{π}{2}, then the number of values of x for which sin x - sin 2 x + sin 3 x = 0, is;$

Solution

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