Find the solution to this equation: 2cos⁡(x)sin⁡(x)+cos⁡(x)=0 The solution should be such that all angles are in radian. for solution the first angle should be between [0,2π) and then the period. And when 2 or more solutions are available then the solution must be in increasing order of the angles.

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Find the solution to this equation:  2cos⁡(x)sin⁡(x)+cos⁡(x)=0  The solution should be such that all angles are in radian. for solution the first angle should be between [0,2π) and then the period.  And when 2 or more solutions are available then the solution must be in increasing order of the angles.

Derrick · Accepted Answer

Step 1  2cos⁡(x)sin⁡(x)+cos⁡(x)=0  cos⁡(x)(2sin⁡(x)+1)=0  cos⁡(x)=0or2sin⁡(x)+1=0  cos⁡(x)=0orsin⁡(x)=−12  first case:  when cos⁡x=0.  cos⁡x=cos⁡(π2)  therefore, x=π2+2kπ  Step 2  when cos⁡x=0.  cos⁡x=cos⁡(3π2)  therefore, x=3π2+2kπ  second case:  when sin⁡x=−12  sin⁡x=sin⁡(5π4)  therefore, x=5π4+2kπ  Step 3  when sin⁡x=−12  sin⁡x=sin⁡(7π4)  therefore, x=7π4+2kπ  therefore the combined solution  is:  x=π2+2kπorx=5π4+2kπorx=3π2+2kπorx=7π4+2kπ  Step 4  therefore the solution of the given equation 2cos⁡(x)sin⁡(x)+cos⁡(x)=0 is:  x=π2+2kπorx=5π4+2kπorx=3π2+2kπorx=7π4+2kπ

Find the solution to this equation: displaystylesqrt{{2}} cos{{left({x}right)}} sin{{left({x}right)}}+ cos{{left({x}right)}}={0} The solution should b

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