Wednesday, 6 August 2014

trigonometry - Can I use cos(2x)=cos2(x)sin2(x) to rewrite 9cos2(x)sin2(x) as 9cos(2x)?



I need to solve for x in

sin(x)=3cos(x)



So I did the following:
sin(x)=3cos(x)sin2(x)=9cos2(x)(squaring both sides)0=9cos2(x)sin2(x)(subtracting sin2(x))



My question is: Am I allowed to use the identity

cos(2x)=cos2(x)sin2(x)
in the equation to make it
0=9cos2(x)sin2(x)0=9cos(2x)



or is that the case that
9cos(2x)9cos2(x)sin2(x)
because the 9 is multiplying the cos only, so that I'm not allowed to use this identity?


Answer



Hint: once squared, you can use the identity:
sin2(x)+cos2(x)=1

To obtain
sin2(x)=9cos2(x)=9(1sin2(x)).
From here you get
sin2(x)=9/10
And you can finish the calculation...



There is no need to use the double-angle identity


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