QR Question 2 on DAT Destroyer 2011

[BTown DDS]

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Does anyone know how the destroyer got to the answer. Here is the question.

sin(44)sec(22)

They say it is 2sin(22), but the way they cancel sec(22) in the answer key doesn't make any sense to me.

 

[mh0000]

sin(44) can be re-written as sin(2x22). You can use the double angle identity to re-write it again into 2sin(22)cos(22).

sec(22) is 1/cos(22)

Combining these two, you get:

2sin(22)cos(22)/cos(22) which the cosines cancel and you get 2sin(22)

 

[basra89]

This is how I understood it..
Sin(2x)= 2sin(x)cos(x).. in this case Sin(44)=2sin(22)cos(22) and we know that sec(x)= 1/cos(x).. Thus, Sin(44)sec(22)= 2sin(22)cos(22)/cos(22).. cancel out cos(22) from both top and bottom and we're left with 2sin(22)... Hope this helps!

 

[BTown DDS]

Thank you. I forgot that sin2(x)=2sin(x)cos(x).