Question

I do not understand these problems. :S
I'd really appreciate the help.

Use trigonometric identities to transform the left side of the equation into the right side.

cot O sin O = cos O

sin^2 O - cos^2O = 2sin^2 O -1

(tan O + cot O)/tan O = csc^2 O

Answer 1

for most of these you have to know your basic trig relationships

tanx = sinx/cosx ; cotx = cosx/sinx
cscx = 1/sinx ; secx = 1/cosx

sin²x + cos²x = 1
and its re-arrangements.

so for the first :
LS = cotOsinO
= (cosO/sinO)(sinO)
= sinO
= RS

Most are this easy.

last one : (I will use x as my angle)
LS
= (sinx/cosx + cosx/ sinx)/(sinx/cosx)
= (sin²x + cos²x)/(sinxcosx) x (cosx/sinx)
= 1/(sinxcosx)(cosx/sinx)
= 1/sin²x
= csc²x
= RS

try the second one, it is even easier.

Answer 2

solve for x to the nearest thousandth: 2tan square x-5tan x-1

Answer 3

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