Quandaries and Queries


name : kris
i am a student
secondary 10-12 or 11th

how to solve the equation
cos 2x = sin x for 0<= x < 360

please solve it
thank you



Hi Kris,

Use the double angle expression for the cosine to get

cos 2x = sin x
cos2(x) - sin2(x) = sin(x)

Then replace cos2(x) by 1 - sin2(x) to get

(1 - sin2(x)) - sin2(x) = sin(x)

which simplifies to

2 sin2(x) + sin(x) - 1 = 0

If you let y = sin(x) then this equation is a quadratic in y which you can solve. This will give you two values for y which then gives you two equations

y = sin(x)

to solve for x.



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