Prove the Identity help

[one2adore30]

Hello,

I would like some help proving the following identity. I have most of it figured out but am stuck on getting the y-1 proven. Here's my problem:


I have completed a couple of steps: quotient identity for tan and difference formula for sin(x-y). How do I get y-1 for -cos sin y?

 

[Dr.Peterson]

Hello,

I would like some help proving the following identity. I have most of it figured out but am stuck on getting the y-1 proven. Here's my problem:
View attachment 16492

I have completed a couple of steps: quotient identity for tan and difference formula for sin(x-y). How do I get y-1 for -cos sin y?

There is no "y-1" there at all! The RHS means "(tan x cot y) - 1".

And there is no "-cos sin y"; you might have a "cos x sin y" meaning cos(x) sin(y), but not "cos(sin y)".

If you still have trouble, please show your work so we can locate the error. (Don't just describe it.)

 

[one2adore30]

Here's what I have so far (in attachment). Thank you for your response.

 

[Dr.Peterson]

Your quotient on the last line is wrong. You only divided the first term of the numerator by the denominator; you have to divide both terms.

 

[one2adore30]

That makes complete sense now that you mention it. Thank you so much for your help. You saved me, Dr. Peterson .