Trigonometric simple equationHow can I solve the following trig equation: sin ⁡ x + 2 cos ⁡ x = 2I tried dividing by cos but it doesn't help much.I also have the following question: sin ⁡ x + p cos ⁡ x = 2 p how much should p be so that this equation has solutions. I know it's related to the first one but I can't figure them out.In the same chapter I have sin 2 ⁡ x + t g 2 x = 3 / 2. I tried solving it with Weierstrass substitution but got to some really complicated equation is there an easier way?

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Trigonometric simple equationHow can I solve the following trig equation:  sin  ⁡  x  +  2  cos  ⁡  x  =  2I tried dividing by   cos but it doesn&#039;t help much.I also have the following question:   sin  ⁡  x  +  p  cos  ⁡  x  =  2  p how much should   p be so that this equation has solutions. I know it&#039;s related to the first one but I can&#039;t figure them out.In the same chapter I have       sin    2    ⁡  x  +  t      g    2    x  =  3      /    2. I tried solving it with Weierstrass substitution but got to some really complicated equation is there an easier way?

Liehm1mm · Accepted Answer

You can use the       sin    2    ⁡  x  +      cos    2    ⁡  x  =  1 in the solution as follows:  sin  ⁡  x  +  2  cos  ⁡  x  =  2  →  2  cos  ⁡  x  =  2  −  sin  ⁡  x    →  (  2  cos  ⁡  x      )    2    =  (  2  −  sin  ⁡  x      )    2      →  4      cos    2    ⁡  x  =  4  +      sin    2    ⁡  x  −  4  sin  ⁡  x    →  4  (  1  −      sin    2    ⁡  x  )  =  4  +      sin    2    ⁡  x  −  4  sin  ⁡  x    →  4  −  4      sin    2    ⁡  x  =  4  +      sin    2    ⁡  x  −  4  sin  ⁡  x    →  5      sin    2    ⁡  x  −  4  sin  ⁡  x  =  0  →  sin  ⁡  x  (  5  sin  ⁡  x  −  4  )  =  0    →  sin  ⁡  x  =  0   or   sin  ⁡  x  =  4      /    5From these   xs can be found, e.g.   sin  ⁡  x  =  0  →  x  =  ±  2  π  k  ,  π  ±  2  π  k and   sin  ⁡  x  =  4      /    5  →  x  =  arcsin  ⁡  (  4      /    5  )  ±  2  π  k  ,  π  −  arcsin  ⁡  (  4      /    5  )  ±  2  π  k

Trigonometric simple equation How can I solve the following trig equation: sin x+2cos x=2

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