Question

Which identity is not used in the proof of the identity?

1 + cot^2 theta = csc^2 theta

Answer 1

here is the proof: http://puu.sh/3cMf2.png

Answer 2

a simple proof is to start with

\[\sin^2(x)+ \cos^2(x) = 1\]

divide each term by sin^2(x) gives

\[1 + \frac{\cos^2(x)}{\sin^2(x)} = \frac{1}{\sin^2(x)}\]

which gives

\[1 + \cot^2(x) = \csc^2(x)\]

so 1 ratio not used is tan^2(x) and perhaps sec^2(x)

Answer 3

i need to know which identity is not used to find the proof. for example, cotangent identity, Pythagorean identity, etc

Answer 4

well the proof doesn't use sec(x) or tan(x)

and it seems a complicated proof...

Answer 5

my options are

cotangent identity
Pythagorean identity
reciprocal identity
and tangent identity

Answer 6

TAngent Identity. It means the usage of tan

Answer 7

Cotangent means the using of various properties of cot: cot^2x+1=cosec^2x
Pythagoran is sin^2x+cos^2x=1
Reciprocal is 1/sin^2x=csc^2x

So only tangent is left.
:)

Answer 8

I love medals! xD

Answer 9

can you help me with one more?

Answer 10

http://puu.sh/3cNKR.png

Answer 11

@kutabs

Answer 12

Option 3 is the only correct one the rest are wrong.

Eg: sin^2x=cos^2x-1
which gives, cos^2x-sin^2=1 (Not possible as sin^2x+cos^2x=1 Phthagoran identity).
Similarly you could prove the others wrong.

Answer 13

Thank you so much!