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1) Simplify the following -- There should be no fractions in your final answer. 

 

      a) (30 sin^3xCosx)/(6cos^2xSinx)

 

      b) (cot^2xSec^2x)/(sinxcot^2x+sinx)

 

2) Solve for Sin(x) be sure to check for all options that are possible (You're only solving for Sinx, not x)

 

2cos^2x(x-pi/2) - 3cos(x-pi/2)-2 = 0

 May 31, 2018
edited by Maplesnowy  May 31, 2018
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1A) reduce what you have to 5sin^2/cos, no fractions, 5 tan sin

1b) always convert everything to sin and cos to make it easy

after doing that and simplifing the top becomes 1/sin^2

the bottom becomes cos^2/sin + sin, common denomenator gives us cos^2+sin^2/sin

hey the top became 1, now we have (1/sin^2)/(1/sin), simplifies into 1/sin or csc with no fractions

 

2) lets convert those cos to sin

factor a - out then convert using cos (pi/2 - x) = sin

-2(sin^2)x+3sinx -2=0

sinx(-2sinx+3) =2

sinx =2 and sinx = 1/2

 May 31, 2018

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