#1 Did note come through properly.


#2 X = log(50.7) =~ 1.7050


#3. True

sin(x)/(1+cos(x)) + cos(x)/sin(x) = 1/sin(x)

sin(x)[sin(x)/(1+cos(x)) + cos(x)/sin(x)] = 1

sin²(x)/(1+cos(x)) + cos(x) = 1

sin²(x)/(1+cos(x)) = 1 - cos(x)

sin²(x) = (1+cos(x))(1 - cos(x))

sin²(x) = 1 - cos²(x) = sin²(x)


#4

[sin^5(x) + sin^4(x) + sin^3(x) + sin^2(x)]/[sin^3(x) + sin^2(x)]

= [sin^5(x) + sin^4(x) + sin^3(x) + sin^2(x)]/{sin^2(x)[sin(x) + sin(x)]}

= [sin^3(x) + sin^2(x) + sin(x) + 1]/[sin(x) + 1]

= [sin^3(x) + sin^2(x)]/[sin(x) + 1] + 1


#5

a.

sin(x)[cos^-1(x) + sin(x)] =

= sin(x)cos^-1(x) + sin(x) =

= sin(x)/cos(x) + sin²(x) =

= tan(x) + sin²(x)


b.

sin²(x) + 2cos(x) =

= sin²(x) + cos²(x) - sin²(x) =

= cos²(x)


c.

[tan²(x) + 1]/sin²(x)

= tan²(x)/sin²(x) + 1/sin²(x)

= 1/cos²(x) + 1/sin²(x)


d.

tan²(x) + 3 - sin²(x)/cos²(x) =

= tan²(x) + 3 - tan²(x) =

= 3


e.

sin²(x) + 3cos²(x) + 2sin²(x) =

= 3cos²(x) + 3sin²(x) =

= 3[cos²(x) + sin²(x)] =

= 3(1) = 3

Sincerely,
Sk1llz

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