Question: Find the principal value of \begin{align} cosec^{-1}\left({2}\right)\end{align}

Answer:

\begin{align} Let \;\; cosec^{-1}\left({2}\right)=y \;\;Then\;\; cosec y = 2 = cosec\left(\frac{\pi}{6}\right)\end{align}

We know that the range of the principal value branch of cosec−1 is

\begin{align} \left[-\frac{\pi}{2},\frac{\pi}{2}\right] - \left(0 \right). \end{align}

Therefore, the principal value of

\begin{align} \frac{\pi}{6}\end{align}

1
0
0
Report?

Report a problem on Specifications:

Email id:

Comments

< Previous Question

Next Question >

SELECT ex_no,question,question_no,id,chapter FROM question_mgmt as q WHERE courseId='3' AND subId='6' AND ex_no!=0 AND status=1 and id!=977 ORDER BY views desc, last_viewed_on desc limit 0,10

Popular questions of class 12 Mathematics

Q: Given an example of a relation. Which is
(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.

Q: Determine whether each of the following relations are reflexive, symmetric and transitive:
(i) Relation R in the set A = {1, 2, 3,13, 14} defined as
R = {(x, y): 3x − y = 0}
(ii) Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x < 4}
(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y): y is divisible by x}
(iv) Relation R in the set Z of all integers defined as
R = {(x, y): x − y is as integer}
(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y): x and y work at the same place}
(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
(d) R = {(x, y): x is wife of y}
(e) R = {(x, y): x is father of y}

Q: Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Q: Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.

Q: Show that the relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive.

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

(i) f : R → R defined by f(x) = 3 – 4x

(ii) f : R → R defined by f(x) = 1 + x²

Q: Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.

Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Q: Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric.

SELECT ex_no,question,question_no,id,chapter FROM question_mgmt as q WHERE courseId='3' AND subId='6' AND ex_no!=0 AND status=1 and id!=977 ORDER BY last_viewed_on desc limit 0,10

Recently Viewed Questions of Class 12 Mathematics

Show that the Signum Function f : R → R, given by

is neither one-one nor onto.

Let A = R – {3} and B = R – {1}. Consider the function f : A → B defined by

. Is f one-one and onto? Justify your answer.

If a line has the direction ratios −18, 12, −4, then what are its direction cosines?

A balloon, which always remains spherical, has a variable diameter

\begin{align} \frac{3}{2}(2x+1)\end{align}

Find the rate of change of its volume with respect to x.

Q: Let R be the relation in the set N given by R = {(a, b): a = b − 2, b > 6}. Choose the correct answer.
(A) (2, 4) ∈ R
(B) (3, 8) ∈R
(C) (6, 8) ∈R
(D) (8, 7) ∈ R

If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.

Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}

Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Write down gof.

Question: Find the principal value of \begin{align} cosec^{-1}\left({2}\right)\end{align}

< Previous Question

Next Question >

Popular questions of class 12 Mathematics

Recently Viewed Questions of Class 12 Mathematics

Comments

Comment(s) on this Question

Important links

Quick Links

Resources

Support