Ask your own question, for FREE!
Mathematics 21 Online
snowflake0531:

#13 @AZ

AZ:

There's a power-reducing identity \(\sin^2 u = \dfrac{1 - \cos(2u)}{2}\)

snowflake0531:

so ^^^ times 2 equals 1/2

snowflake0531:

1/2 = cos(2x)

AZ:

how? \( 2 \times \dfrac{1-\cos(2\cdot 2x)}{2} = \dfrac{1}{2}\)

snowflake0531:

so 1/2 = cos(4x)

AZ:

oh wait my bad, it should be equal to 1 not 1/2 so cos(4x) = 1

AZ:

your question has 1 in it, if you check your screenshot

snowflake0531:

But there's a 2 before the sin^2(2x) so it's still 1/2

snowflake0531:

wait nvmd

AZ:

... \( 2\sin^2(2x) = 1\) \( 2 \left( \dfrac{1-\cos(2\cdot 2x)}{2}\right) = 1\) \( \cancel{2}\left( \dfrac{1-\cos(2\cdot 2x)}{\cancel{2}}\right) = 1\)

snowflake0531:

e.e

snowflake0531:

how'd you do the cross out thing

snowflake0531:

but ye 1-cos(4x)=1 cos(4x)=0

snowflake0531:

and pi/2 and 3pi/2 is when cos =0

snowflake0531:

so then pi/2 + 2pik

AZ:

but remember, it's cos(4x) so if we said cos(u) = 0 then u = pi/2 + \(\pi\)k but then u = 4x so you have to divide by 4

AZ:

it's every pi, not 2pi

snowflake0531:

so pi/8 +pi k

AZ:

you also have to divide pi*k by 4 as well

snowflake0531:

kk

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!