How do you solve #3sin^2(x) = cos^2(x)#?

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Answer 1 · 2018-05-02T08:48:10

#x = 30, 150, 210, 330#

I'll be using #theta# to substitute as #x# and assuming the range of the value of #theta# is #0-360# degrees.

#3sin^2theta = cos^2theta#

By applying the formulae :

#sin^2theta + cos^2theta = 1#

#=> sin^2theta = 1-cos^2theta#

Thus,

#3 (1 - cos^2theta) = cos^2theta#

#=> 3-3cos^2theta = cos^2theta#

#=> 3 = 4 cos^2theta#

#=> 3/4 = cos^2theta#

#=> +-sqrt(3/4) = cos theta#

#=> cos theta = sqrt (3/4) or cos theta = -sqrt(3/4)#

#:. theta : 30 , 150, 210, 330# in degrees.

You can check if the answer is correct by inserting the values calculated.

There you go, finished! :)