Saved Bookmarks
| 1. |
If `sin^(-1)x+sin^(-1)y+sin^(-1)z=pi` then the value of `xsqrt(1-x^(2))+ysqrt(1-y^(2))+zsqrt(1-z^(2))`A. 2xyzB. `x^(2)+y^(2)+z^(2)`C. `xy+yz+zx`D. none of these |
|
Answer» Let `sin^(-1) x =A sin^(-1) y = B and sin^(-1) z = C` Then `x= sin A, y sin B z = sin C` Also `sin^(-1)x+ sin^(-1) y + sin^(-1)z=pi` `rarr A+B+C=pi` `rarr sin 2A + sin 2B + sin 2C =4 A sin B sin C` `rarr sin A cos A + sin B cos B + sin C cos C =2 sin A sin B sin C` `rarr xsqrt(1-x^(2))+ysqrt(1-y^(2))+zsqrt(1-z^(2))=2xyz` |
|