Question

Prove
(1+tan^2(u))(cos^2(u))=1

Answer 1

Does anyone know the identities need to slove theses?

Answer 2

Remember the identity:\[\sec^{2}u = 1+\tan^{2}u\](That identity is found by dividing the pythagorean identity by cos^2u instead of sin^2u) Replace 1+tan^2u in your equation to get:\[(\sec^{2}u)(\cos^{2}u) = 1\]Write sec in terms of cos:\[\frac{1}{\cos^{2}u} \times \frac{\cos^{2}u}{1} = 1\] The cosines cancel, leaving you with \[1 = 1\] It looks like all of your problems require the pythagorean identity and derivations of it. I would memorize them if I were you

Answer 3

so the identities are
sin^2x+cos^2x=1
tan^2x+1=sec^2x
1+cot^2x=csc^2x

Answer 4

Yes!

Answer 5

Thanks, This is all brand new to me.
If I were to prove (1+tan^2(v)(1-sin^2)(v))=1 would it be the following?
sec^2(v)(1-sin^2(v)=1
sec^2(v)(cos^2(v))=1
1/cos times cos/1=1
1=1