Question

Verify identity
cot(θ)+tan(θ)=csc(θ)sec(θ)

Any hints how to start? I'm completely stuck on this one... Thanks.

Answer 1

Last Resort: Change everything to sine and cosine.

Answer 2

ok let me see

Answer 3

ok so i got

(cos(θ)+sin(θ))/(cos(θ)+sin(θ))=(1)/(cos(θ)sin(θ))

Answer 4

stuck again

Answer 5

left side will be 1

Answer 6

what do i do with right side?

Answer 7

the addition of fraction is not right.
\[\frac{a}{b} + \frac{b}{a} \color{red}\neq \frac{a+b}{b+a}\]

Answer 8

you right... ok, let me redo it, thx

Answer 9

ok, so when i did multiply it as it should be I got (1)/(cos(θ)sin(θ)) on both sides. is that correct?

Answer 10

\[\frac{ \cos \theta }{ \sin \theta } + \frac{ \sin \theta }{ \cos \theta } \]

then multiply by the common factors so first fraction by cos theta and the second by sin theta so you get : \[\frac{ \cos^2 \theta + \sin^2 \theta }{ \sin \theta \cos \theta}\]


according to the pythagorean the numenator will equal 1 so you get 1/ sin theta cos theta

Answer 11

thats what i got, perfect thx

Answer 12

on the other side csc theta sec theta can be simplified to: (1/sin theta ) (1/cos theta)
so you get 1 / sin theta cos theta QED

Answer 13

QED and the trigie biggie

Answer 14

EXACTLY