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Stuck on how to go forward with this proof. Teacher advised starting again and cross multiplying then cancelling the fractions, but I’m being stubborn. Is there any way to go forward with this way?

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(edited 11 months ago)

Reply 1

mqb2766

21

Original post

by rememberemi

Stuck on how to go forward with this proof. Teacher advised starting again and cross multiplying then cancelling the fractions, but I’m being stubborn. Is there any way to go forward with this way?

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Sure, youve one cosec(x) on the left so the sum of the other two terms must also be cosec(x) for the identity to hold. So you want them to be 1/sin(x). The third term has a denominator 1+cos(x). Can you multiply the fraction (top and bottom) by something so that becomes something like sin(x), or something very similar? You could have done this to the first line (lhs of the question) and it should be just a couple of lines.

Reply 2

username7622592

OP

14

Original post

by mqb2766

Sure, youve one cosec(x) on the left so the sum of the other two terms must also be cosec(x) for the identity to hold. So you want them to be 1/sin(x). The third term has a denominator 1+cos(x). Can you multiply the fraction (top and bottom) by something so that becomes something like sin(x), or something very similar?

I didn’t think to think of it that way! I changed cotx back to cosx/sinx and then cross multiplied and expanded and cancelled to get 1/sinx! Thank you very much. You always seem to answer my maths questions, seriously you’re super helpful, thanks again! 😄

Reply 3

mqb2766

21

Original post

by rememberemi

I didn’t think to think of it that way! I changed cotx back to cosx/sinx and then cross multiplied and expanded and cancelled to get 1/sinx! Thank you very much. You always seem to answer my maths questions, seriously you’re super helpful, thanks again! 😄

NP. Tbh from the original identity you have the first term on the left
(1+cos) / sin
so "guessing" the answer, the other term on the left must be (1-cos)/sin and then numerator pretty much gives it.

Reply 4

Muttley79

20

Original post

by rememberemi

I didn’t think to think of it that way! I changed cotx back to cosx/sinx and then cross multiplied and expanded and cancelled to get 1/sinx! Thank you very much. You always seem to answer my maths questions, seriously you’re super helpful, thanks again! 😄

Please don't get into the habit of cross multiplying ...people end up using it when it's inappropriate.

Multiply through by a denominator -

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