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
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.
solve for x to the nearest thousandth: 2tan square x-5tan x-1
12
Sure! I'll walk you through each problem and explain how to use trigonometric identities to transform the left side of the equation into the right side.
1. cot O sin O = cos O:
To simplify the left side, we can rewrite cot O as 1/tan O. Therefore, the equation becomes (1/tan O) * sin O = cos O. Now, we can use the identity sin O = 1/csc O to rewrite sin O. So, the equation becomes (1/tan O) * (1/csc O) = cos O. Now, we can multiply the terms on the left side, giving us (1/(tan O * csc O)) = cos O. Finally, we remember that tan O = sin O / cos O and csc O = 1/sin O, so we can substitute these values in, giving us 1/(sin O / cos O * 1/sin O) = cos O. After simplifying, we get cos O = cos O.
2. sin^2 O - cos^2 O = 2sin^2 O - 1:
We can start with the left side of the equation. We know that sin^2 O = 1 - cos^2 O, which is an identity. So, we can substitute this value into the left side, giving us (1 - cos^2 O) - cos^2 O. Simplifying, we get 1 - 2cos^2 O. Now, let's simplify the right side. We have 2sin^2 O - 1. Using the identity sin^2 O = 1 - cos^2 O again, we can rewrite the right side as 2(1 - cos^2 O) - 1. Simplifying this, we get 2 - 2cos^2 O - 1. Combining like terms, we have 1 - 2cos^2 O. Therefore, the left side of the equation is equal to the right side.
3. (tan O + cot O)/tan O = csc^2 O:
Let's start with the left side of the equation. We know that cot O = 1/tan O. So, we can rewrite the equation as (tan O + 1/tan O)/tan O. To simplify this expression, we can multiply both the numerator and denominator by tan O. This gives us ((tan O)^2 + 1)/tan O^2. Now, recalling the Pythagorean identity tan^2 O = 1 - cos^2 O, we can substitute this value in for (tan O)^2 in the numerator. This gives us (1 - cos^2 O + 1)/tan O^2. Simplifying, we have (2 - cos^2 O)/tan O^2. Now, we can use the identity csc O = 1/sin O, which gives us 1/sin^2 O. Therefore, the right side of the equation is csc^2 O.