Solve the given equation. If there is no solution, enter NO SOLUTION: cos2x=5sinx-2?

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Answer 1 · 2017-12-03T00:48:54

Answer: #x=pi/6+2pik,(5pi)/6+2pik#, #k in ZZ#

Solve #cos2x=5sinx-2#

Note that #cos(2x)=1-2sin^2(x)#

Substituting in, we have:
#1-2sin^2(x)=5sinx-2#

Moving everything to one side:
#2sin^2(x)+5sinx-3=0#

We now have a quadratic which we can factor:
#(2sinx-1)(sinx+3)=0#

So, we have that #sinx=1/2# or #sinx=-3#, clearly the latter is not possible since #sinx in [-1,1]#

Therefore #x=pi/6+2pik,(5pi)/6+2pik#, #k in ZZ#