Question

Which value of theta is not in the domain of validity for csc theta =1/sin theta

Answer 1

Verify each identity give the domain of validity for each identity. It is very used to prove these identities for any value of theta in the domain. So I just specify the domain and leave verification for you to do t with standard values or on calculator. Because verification is an endless process. Proof is not. As proof seems to be simple I will do that which will amount to verification as well

Answer 2

Answer with explanation:

The given expression is:

`\csc \Theta^(\circ) =(1)/(\sin \Theta^(\circ))`

Domain of Cosec theta,will be all values in Radian or degree except at the point where,

→sine(theta)≠ 0.

If theta is in either Degrees or in Radian, then

`\Theta\\eq k \pi ,\text{Where k, is any Integer}`

The value of theta which is not in the domain for the validity of

`\csc \Theta^(\circ) =(1)/(\sin \Theta^(\circ))`

is, →→Theta(Ф)≠ k π, for any integer ,k.