Evaluate: `sin(1/2cos^(-1)4/5)`A. `1/sqrt(5)`B. `2/sqrt(5)`C. `1/sqrt(10)`D. `2/sqrt(10)`

Evaluate: `sin(1/2cos^(-1)4/5)`A. `1/sqrt(5)`B. `2/sqrt(5)`C. `1/sqrt(

1.	Evaluate: `sin(1/2cos^(-1)4/5)`A. `1/sqrt(5)`B. `2/sqrt(5)`C. `1/sqrt(10)`D. `2/sqrt(10)`
Answer» Correct Answer - C Let `cos^(-1)4/5=x`, where `x in [0,pi]`. Then, `cosx=4/5`. Since, `x in [0,pi] to 1/2 x in [0,pi/2] rArr sin1/2 x gt 0`. `sin(1/2cos^(-1)4/5) = sin1/2x =sqrt((1-cosx)/2)=sqrt((1-4/5)/(2))=1/sqrt(10)`.

Range of `"cosec"^(-1)x` isA. `(-pi/2,pi/2)`B. `[-pi/2,pi/2]`C. `[-pi/2,pi/2]-{0}`D. none of these
The value of `"cosec"^(-1)("cosec"(4pi)/3)` isA. `(3pi)/4`B. `pi/4`C. `-pi/4`D. none of these
Find the principalvalue of `sec^(-1)((-2)/(sqrt(3)))`A. `pi/6`B. `-pi/6`C. `(5pi)/6`D. `(7pi)/6`
The principal value of `"cosec"^(-1)(-sqrt(2))` isA. `-pi/4`B. `(3pi)/4`C. `(5pi)/4`D. none of these
Find the principal value of each of the following: i) `cos^(-1)(-1/sqrt(2))`, ii) `cos^(-1)(-1/2)`, iii) `cot^(-1)(-1/sqrt(3))`
Find the principal value of each of the following: i) `cot^(-1)(-sqrt(3))` ii) `sec^(-1)(-sqrt(2))` iii) `"cosec"^(-1)(-1)`.
The principal value of `cot^(-1)(-1)` isA. `-pi/4`B. `pi/4`C. `(5pi)/4`D. `(3pi)/4`
Find the principal valuesof each of the following:`cot^(-1)(-sqrt(3))`(ii) `cot^(-1)(sqrt(3))`A. `-pi/6`B. `pi/6`C. `(7pi)/6`D. `(5pi)/6`
If `tan^(-1)x=pi/4-tan^(-1)(1/3)` then `x` isA. `1/2`B. `1/4`C. `1/6`D. none of these
The value of `tan^(-1)(tan(8*pi/6))` isA. `(7pi)/6`B. `(5pi)/3`C. `pi/3`D. none of these