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# c3 trig identities watch

1. prove cosec(theta) - sin(theta) = cot(theta)cos(theta)

cosec(theta) - sin(theta) = 1/sin(theta) - sin(theta)

= (1 - sin^2(theta)) / sin(theta) = (cos^2(theta)) / sin(theta)

I'm guessing that this is correct, but i don't understand how the cos(theta) can be isolated from cot(theta) to get it = to RHS. Can someone explain?
2. Use the identity cot(theta) = cos(theta)/sin(theta):

cos^2(theta) / sin(theta)

= cos(theta)/sin(theta) * cos(theta)

= cot(theta)cos(theta)
3. (Original post by AndyOC)
prove cosec(theta) - sin(theta) = cot(theta)cos(theta)

cosec(theta) - sin(theta) = 1/sin(theta) - sin(theta)

= (1 - sin^2(theta)) / sin(theta) = (cos^2(theta)) / sin(theta)

I'm guessing that this is correct, but i don't understand how the cos(theta) can be isolated from cot(theta) to get it = to RHS. Can someone explain?
Remember that

and so

4. (Original post by Indeterminate)
Remember that

and so

(Original post by Pronged Lily)
Use the identity cot(theta) = cos(theta)/sin(theta):

cos^2(theta) / sin(theta)

= cos(theta)/sin(theta) * cos(theta)

= cot(theta)cos(theta)
Ah yeah of course, thanks for the help!
5. 1/sin(theta) - sin(theta)

= (1 - sin^2(theta)) / sin(theta)

How did you go from this step to this as if you times both sides by Sin(Theta) it will be only 1-sin(squared)(Theta).
6. (Original post by Chocolatemousse)
1/sin(theta) - sin(theta)

= (1 - sin^2(theta)) / sin(theta)

How did you go from this step to this as if you times both sides by Sin(Theta) it will be only 1-sin(squared)(Theta).
It's not an equation where you times both sides by something, it's just combining fractions:

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