Question

Use basic identities to simplify the expression. (6 points)

sin^2θ+ tan^2θ+ cos^2θ

Answer 1

remember the very first one

sin^2 + cos^2 = 1

from the unit circle pythagorean theorem

Answer 2

yes

Answer 3

and there is another pythagorean theorem on the unit circle,

tan^2 + 1^2 = sec^2

Answer 4

after what you do?

Answer 5

sin^2θ+ tan^2θ+ cos^2θ

they just want you to simplify that using the identities, notice it already has sin^2 + cos^2, you can replace that with 1

Answer 6

then use the other pythagorean one i mentioned to finish it up

Answer 7

so it would equal tan theta

Answer 8

you start with
sin^2(a) + cos^2(a) + tan^2(a)

use the sin^2(a) + cos^2(a) = 1 identity
gives

1 + tan^2(a)

use the tan^2(a) + 1 = sec^2(a) identity
gives

sec^2(a)

Answer 9

here is the geometry of where the two identity come from, the pythagorean theorem of these lines