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Novosadov [1.4K]
3 years ago
5

Verify the basic identity. What is the domain of validity? cot theta = cos theta csc theta

Mathematics
2 answers:
Kay [80]3 years ago
6 0
Cot x = cos x csc x
1/tan x = cosx (1/sin x)
1/(sin x / cos x) = cos x / sin x
cos x / sin x = cos x / sin x

The domain of validity is all real number values of x except for sin x = 0.
Ede4ka [16]3 years ago
4 0
<h2>Answer:</h2>

<u>Domain of validity--</u>

All real numbers except nπ where n belongs to integers.

( Since,

\sin n\pi=0\ for\ all\ n\ belonging\ to\ integers )

<h2>Step-by-step explanation:</h2>

We are asked to prove the trignometric identity:

        \cot \theta=\cos \theta\csc \theta

We know that the cotangent function is given by the formula:

          \cot \theta=\dfrac{\cos \theta}{\sin \theta}

Also we know that:

\csc \theta=\dfrac{1}{\sin \theta}

Hence, we have:

\cot \theta=\cos \theta\times \dfrac{1}{\sin \theta}\\\\\\\cot \theta=\cos \theta\csc \theta

Now, the domain of validity i.e. the values for which the cotangent function is defined is the set of all the real  number except where sine function is zero.

Since the sine function appear in the denominator and for a function to be well defined denominator term must be non-zero.

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