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AfilCa [17]
3 years ago
14

For sin2x+cosx=0, use a double-angle or half-angle formula to simplify the equation and then find all solutions of the equation

in the interval [0,2π).
Mathematics
1 answer:
Archy [21]3 years ago
4 0

Answer:

Step-by-step explanation:

Given is a trignometric equation in x, as

sin2x+cosx=0

TO make it in one trig ratio, we can replace sin2x as 2sinx cosx

WE get now

2sinxcosx+cosx=0\\

cosx(2sinx+1)=0\\cosx=0, sinx =-0.5\\

Principal solution is x=\frac{\pi}{2} , \frac{-\pi}{6}

x = ±π/2 + 2kπ, where k is any integer or

x=±pi/6 +k pi, where k is any integer.

General solution is

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