InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `sin^(-1)a+sin^(-1)b+sin^(-1)c=pi,`then the value of `asqrt((1-a^2))+bsqrt((1-b^2))+sqrt((1-c^2))`will be`2a b c`(b) `a b c`(c) `1/2a b c`(d) `1/3a b c`A. `2 abc`B. `abc`C. `(1)/(2) abc`D. `(1)/(3) abc` |
|
Answer» Correct Answer - A Let `sin^(-1) a = A, sin^(-1) b = B and sin^(-1) c = C` `rArr sin A = a, sin B = b, sin C = c` and `A + B + C = pi` `rArr sin 2A + sin 2B + sin 2C` `= 4 sin A sin B sin C`....(i) `rArr sin A cos A + sin B cos B + sin C cos C` `= 2 sin A sin B sin C` `rArr sin A sqrt(1 - sin^(2) A) + sin B sqrt(1 - sin^(2) B)` `+ sin C sqrt(1 - sin^(2) C) = 2 sin A sin B sin C` ..(ii) `rArr asqrt((1 - a^(2))) + bsqrt((1 -b^(2))) + c sqrt((1 - c)^(2)) = 2abc` Alternatively : Let `a = (1)/(sqrt2), b = (1)/(sqrt2), c =1` Then `asqrt(1 -a^(2)) + bsqrt(1 -b^(2)) + csqrt(1 -c^(2))` `= (1)/(sqrt2) sqrt(1 - (1)/(2)) + (1)/(sqrt2) sqrt(1 -(1)/(2)) + 1 sqrt(1 -1) = 1` `= 2. (1)/(sqrt2). (1)/(sqrt2) .1` |
|