Advertisements
Advertisements
Question
Find the value of `sin^-1 (- 1) + cos^-1 (1/2) + cot^-1 (2)`
Solution
x = `sin^-1 (1)`
sin x = `-1 = sin(- pi/2)`
x = `- pi/2`
y = `cos^-1 (1/2)`
cos y = `1/2 = cos pi/3`
y = `pi/3`
z = `cot^-1 (2)`
cot z = 2
z = `cot^-1 (2)` is constant.
`sin^-1(- 1) + cos^-1(1/3) + cot^-1(2)`
= `- pi/2 + pi/3 + cot^-1(2)`
= `- (3pi + 2pi)/6 + cot^-1(2)`
= `cot^-1(2) - pi/6`
APPEARS IN
RELATED QUESTIONS
Find the principal value of `sec^-1 (2/sqrt(3))`
Find the principal value of `cot^-1 (sqrt(3))`
Find the principal value of `"cosec"^-1 (- sqrt(2))`
Find the value of `tan^-1 (sqrt(3)) - sec^-1 (- 2)`
Find the value of `cot^-1(1) + sin^-1 (- sqrt(3)/2) - sec^-1 (- sqrt(2))`
Choose the correct alternative:
The value of sin–1(cos x), 0 ≤ x ≤ π is
Choose the correct alternative:
If x = `1/5`, the value of `cos(cos^-1x + 2sin^-1x)` is
Choose the correct alternative:
If `sin^-1x + "cosec"^-1 5/4 = pi/2`, then the value of x is
Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation cos–1 (x) – 2sin–1(x) = cos–1 (2x) is equal to ______.
Given that the inverse trigonometric function take principal values only. Then, the number of real values of x which satisfy `sin^-1((3x)/5) + sin^-1((4x)/5) = sin^-1x` is equal to ______.
