Class 12 Mathematics - Chapter Inverse Trigonometric Functions NCERT Solutions | Find the principal value of \begin{align
Find the principal value of \begin{align} cosec^{-1}\left({-\sqrt2}\right)\end{align}
\begin{align} Let \;\; cosec^{-1}\left({-\sqrt2}\right)=y \;\;Then\;\; cosec y = -{\sqrt2} =- cosec\left(\frac{\pi}{4}\right) = cosec\left(-\frac{\pi}{4}\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) and \;\;cosec\left(-\frac{\pi}{4}\right) = -\sqrt2.\end{align}
Therefore, the principal value of
\begin{align} cosec^{-1}\left(-\sqrt2\right) is -\frac{\pi}{4}\end{align}
More Questions From Class 12 Mathematics - Chapter Inverse Trigonometric Functions
- Q:- Find the principal value of \begin{align} tan^{-1}\left(-\sqrt3\right)\end{align}
- Q:- Find the principal value of \begin{align} sec^{-1}\left(\frac{2}{\sqrt3}\right)\end{align}
- Q:- Find the value of if \begin{align} tan^{-1}\sqrt3 - sec^{-1}(-2)\end{align}
is equal to
\begin{align} (A) \pi \;\;(B) -\frac{\pi}{3}\;\; (C) \frac{\pi}{3} \;\;(D) \frac{2\pi}{3}\end{align} - Q:- Find the principal value of \begin{align} cos^{-1}\left(-\frac{1}{\sqrt2}\right)\end{align}
- Q:- Find the principal value of \begin{align} cos^{-1}\left(-\frac{1}{2}\right)\end{align}
- Q:- Find the principal value of \begin{align} cos^{-1}\left(\frac{1}{2}\right) + 2sin^{-1}\left(\frac{1}{2}\right)\end{align}
- Q:- Find the principal value of \begin{align} sin^{-1}\left(-\frac{1}{2}\right)\end{align}
- Q:- Find the principal value of \begin{align} cos^{-1}\left(\frac{\sqrt3}{2}\right)\end{align}
- Q:- Find the principal value of \begin{align} tan^{-1} (1) + cos^{-1}\left(-\frac{1}{2}\right) + sin^{-1}\left(-\frac{1}{2}\right)\end{align}
- Q:- Find the principal value of \begin{align} cot^{-1}\left(\sqrt3\right)\end{align}
Popular Questions of Class 12 Mathematics
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\begin{vmatrix} \mathbf{2} & \mathbf{4} \\ \mathbf{-5} & \mathbf{-1} \end{vmatrix} - 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
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(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:- Find the rate of change of the area of a circle with respect to its radius r when
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(b) r = 4 cm - Q:-
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
Recently Viewed Questions of Class 12 Mathematics
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The total revenue in Rupees received from the sale of x units of a product is given by
R (x) = 3x2 + 36x + 5. The marginal revenue, when x = 15 is
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A balloon, which always remains spherical, has a variable diameter
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