Question

precalc question

Answer 1

\[\frac{ \sec \Theta }{ 1-\sin \Theta }= \frac{ 1+\sin \Theta }{ \cos^{3} \Theta }\]

Answer 2

we cannot manipulate the properties of the trig identities so does anyone know how to solve it

Answer 3

Do you want to solve or prove an identity?

Answer 4

prove an identity

Answer 5

cos^2x =1-sin^2 x =(1-sin x)(1+sinx)

Answer 6

but we cannot manipualte identities like i tried multiplying by the conjugate on the left side which gave 1-sin^2theta but we cannot use that to say it equals cos^2 theta

Answer 7

Sec theta = 1/cos theta

substitute that for sec theta, and simplify.

Answer 8

yeah our teacher said we cannot manipulate the identity like that

Answer 9

That's not true; you probably misunderstood what your teacher said.

sec theta = 1/cos theta, is a reciprocal function property, which is permissable to substitute when proving an identity.

Answer 10

like we have to leave it as sin^2+cos^2=1

Answer 11

he said making it 1-sin^2=cos^2 requires a whole separate proof which we are not allowed to do

Answer 12

There is no way to prove that identity if you do not substitute 1/cos theta for sec theta.