Question

properties of inverse trigonometry
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Answer 1

Answer:

Important Properties of Inverse Trigonometric Functions

Sin−1(x) = cosec−1(1/x), x∈ [−1,1]−{0}

Cos−1(x) = sec−1(1/x), x ∈ [−1,1]−{0}

Tan−1(x) = cot−1(1/x), if x > 0

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Answer 2

Answer:

There are a few inverse trigonometric functions properties which are crucial to not only solve problems but also to have a deeper understanding of this concept. To recall, inverse trigonometric functions are also called “Arc Functions,” since for a given value of a trigonometric function; they produce the length of arc needed to obtain that particular value. The range of an inverse function is defined as the range of values the inverse function can attain with the defined domain of the function. The domain of a function is defined as the set of every possible independent variable where the function exists. Inverse Trigonometric Functions are defined in a certain interval.

Considering the domain and range of the inverse functions, following formulas are important to be noted:

sin(sin−1x) = x, if -1 ≤ x ≤ 1

cos(cos−1x) = x, if -1 ≤ x ≤ 1

tan(tan−1x) = x, if -∞ ≤ x ≤∞

cot(cot−1x) = x, if -∞≤ x ≤∞

sec(sec−1x) = x, if -∞ ≤ x ≤ -1 or 1 ≤ x ≤ ∞

cosec(cosec−1x) = x, if -∞ ≤ x ≤ -1 or 1 ≤ x ≤ ∞