Question

TRIG QUESTION, SOMEONE PLEASE HELP
prove: tan^2Θ * cos^2Θ + cos^2Θ= 1
please show work and thank you so much in advance

Answer 1

tan theta= sin theta / cos theta
so, tan^2 theta* cos^2 theta= sin^2 theta
i guess you already know sin^2 theta+ cos^2 theta=1

Answer 2

or else you can draw the diagram and use pythagoras theorem

Answer 3

I used the trig identities to solve this. tan^2 converts to (or is equivalent to) \[\tan ^{2}\theta=\frac{ \sin ^{2}\theta }{ \cos ^{2} }\]Oops, for some reason it left off the theta with the cosine. Oh well. Now, subbing in that identity you get \[\frac{ \sin ^{2}\theta }{ \cos ^{2}\theta }\times \cos ^{2}\theta +\cos ^{2}\theta =1\]Now you can cancel out the cos^2 like this

Answer 4

and you're left with sin^2 theta + cos^2 theta = 1 which is true, right?