Can someone help me to solve these 2 questions.?

Question

1.Find the min and max value of 2(cosx+2)^2-9
2.Which one is the correct perfect square of 2(cos^2 x-5 cosx):
*2(cosx-5/2)^2-27/2
*2(cosx-5/2)^2-29/4

Answer 1

1) just put the Min and Max value of Cosx :
min { 2(cosx+2)^2 - 9 }= 2( (-1) +2 )^2 - 9 = -7
max { 2(cosx+2)^2 - 9 }= 2( (1) + 2)^2 - 9 = 9

2) i think your question is: which one is the correct perfect square of 2( (cosx)^2 - 5cosx )

then the answer is:

let cosx = y
then : 2( (cosx)^2 - 5cosx ) =
2( y^2 - 5y ) = 2 ( (y -5/2 )^2 - 25/4) =
2 (y - 5/2)^2 - 25/2 =
2 (cosx-5/2)^2 - 25/2

Answer 2

1. Max [ 2(cosX + 2)^2 - 9 :
as you know the maximum of cos X is +1 so we replace cosx with 1 :
2 (1+2)^2 - 9 = 18 - 9 = 9

2. your question is not comprehensible enough.

Answer 3

1. The min and max value of 2(cosx+2)^2-9 in the interval [-180 , 180] its -7 , when sin function calculated in degrees.

2. Sorry for the second answer.

Answer 4

1)
max = 9
min = -7