English
Tamil Nadu Board of Secondary EducationHSC Science Class 12

Find the value, if it exists. If not, give the reason for non-existence sin-1(cosπ) - Mathematics

Advertisements
Advertisements

Question

Find the value, if it exists. If not, give the reason for non-existence

`sin^-1 (cos pi)`

Sum
Advertisements

Solution

`sin^-1 (cos pi) = sin^-1(- 1)`

= `- sin^-1 (1)`

= `- pi/2`  ......[∵ cos π = – 1]

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Inverse Trigonometric Functions - Exercise 4.5 [Page 166]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 4 Inverse Trigonometric Functions
Exercise 4.5 | Q 1. (i) | Page 166

RELATED QUESTIONS

Prove the following: 

3cos−1x = cos−1(4x3 − 3x), `x ∈ [1/2, 1]`


Write the function in the simplest form: `tan^(-1)  1/(sqrt(x^2 - 1)), |x| > 1`


Write the following function in the simplest form:

`tan^(-1) (sqrt((1-cos x)/(1 + cos x)))`, 0 < x < π


Find the value of the given expression.

`sin^(-1) (sin  (2pi)/3)`


Prove that:

`tan^(-1) sqrtx = 1/2 cos^(-1)  (1-x)/(1+x)`, x ∈ [0, 1]


If cos-1 x + cos -1 y + cos -1 z = π , prove that x2 + y2 + z2 + 2xyz = 1.


Find the value of `sin^-1[cos(sin^-1 (sqrt(3)/2))]`


Solve: `tan^-1x = cos^-1  (1 - "a"^2)/(1 + "a"^2) - cos^-1  (1 - "b"^2)/(1 + "b"^2), "a" > 0, "b" > 0`


Prove that cot–17 + cot–18 + cot–118 = cot–13


Show that `2tan^-1 {tan  alpha/2 * tan(pi/4 - beta/2)} = tan^-1  (sin alpha cos beta)/(cosalpha + sinbeta)`


If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.


The value of the expression `tan (1/2 cos^-1  2/sqrt(5))` is ______.


If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.


`"sin" {2  "cos"^-1 ((-3)/5)}` is equal to ____________.


The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:

Measure of ∠CAB = ________.


The Simplest form of `cot^-1 (1/sqrt(x^2 - 1))`, |x| > 1 is


What is the simplest form of `tan^-1  sqrt(1 - x^2 - 1)/x, x ≠ 0`


The set of all values of k for which (tan–1 x)3 + (cot–1 x)3 = kπ3, x ∈ R, is the internal ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×