Question

Can someone explain to me how to solve this? I dont understand how to do it? I have to verify the identity.
sec^2 x = 1 + tan^2 x

Answer 1

Pythagoreas' theorem

draw the triangle and match it all up !!!!

Answer 2

....with the definitions of sec and tan, of course

Answer 3

@Directrix so then would it break up into the
(sin^2x)/(sin^2x)+(cos^2x)/(sin^2x)=1/(sin^2x) equation?

Answer 4

@Directrix i did study it but i just dont completely understand how to solve it or work it out

Answer 5

i have studied the sin^2(theta)+cos^2(theta)=1 but i dont understand how to verify the identity

Answer 6

Pythagoreas' theorem

Answer 7

@IrishBoy123 so then to verify it do i make it
(sin^2x)/(sin^2x)+(cos^2x)/(sin^2x)=1/(sin^2x) ?

Answer 8

try it the other way round

you have mjust proved that \(1 + \cot^2 x = \sec^2 x\)

Answer 9

which means "you're doing good"

Answer 10

what do you mean by the other way around? @IrishBoy123

Answer 11

sin^2 x + cos^2 x = 1

Divide each term by cos^2 x

sin^2 x + cos^2 x = 1
----- ------- -----
cos^2 x cos^2 x cos^2 x

tan^2 x + 1 = sec^2 x


You need to know the basic trig identities for this to make sense.

@Yessy16c