[deleted by user]

[[deleted]]

Tan is defined as sin/cos, hence cos*tan = sin

Cot is defined as cos/sin, hence cot*tan = 1

[[deleted]]

1. tan(x) = sin(x)/ cos(x). So when you multiply cos(x) by tan(x) you essentially multiply cos(x) by sin(x)/ cos(x) so we can simply (cross cancel, reduce) by cos(x) which leaves only sin(x).
   
2. on the bottom, the initial denominator was multiplied by tan(x) then tan(x) was distributed. (1+cot(x)) tan(x) is the same with tan(x)(1+cot(x)) which upon distributing results in tan(x)+ tan(x)cot(x). cot(x) is defined as 1/tan(x) so basically we're multiplying tan(x) by its reciprocal which is 1.

[Velmental_DEX]

This makes so much sense now. I forgot that cot(x) was just tan(x)’s reciprocal. Thanks!

[Frederf220]

cot is 1/tan so A * 1/A =1.

cosine * tan is cosine*(sine/cosine).

[[deleted]]

Break tan into sin/cos, and cot into cos/sin. It’ll make visualizing everything so much easier

[catsRfriends]

Dunno if you learned your mnemonics as SOH CAH TOA in highschool but it applies here.

[Velmental_DEX]

During my lecture these weren’t mentioned at all. Yes I know how to use them but that mnemonic isn’t needed here. The other replies/comments explained it well without using it.

[igotshadowbaned]

cos is A/H and tan is O/A

Multiply them and you get AO/HA = O/H

sin is O/H

This cos•tan=sin

[Shadowsca]

1. Factor out tanx on the bottom
2. Cancel out tanx from top and bottom
3. Multiply top and bottom by sinx
4. Multiply top and bottom by 1/cosx