The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin-1(sinx), -pie<=x<=pie, is:

Question

The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin-1(sinx), -pie<=x<=pie, is:

The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^-1(sinx), -pie<=x<=pie, is:

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

1+cos2x= 2cos²x;

using this and putting it in given expression I will get cosx = sin^-1sinx. ,-π <= x <= π

Now draw the curves of cosx for -π <= x <= π and also draw the curve of sin^-1sinx for -π <= x <= π and find the no. of intersection points of the curve. They will intersect at two points only.

So, Ans is 2.