A) \[\pm cosx\text{ }cosy\text{ }cosz\]
B) \[\pm \sin x\,\sin y\,sinz\]
C) \[\pm sinx\text{ }cosy\text{ }cosz\]
D) \[\pm \sin x\,siny\,cosz\]
Correct Answer: A
Solution :
(a): \[\left( 1+\sin x \right)\left( 1+\sin y \right)\left( 1+sinz \right)\] \[=\left( 1-\sin x \right)\left( 1-\sin y \right)\left( 1-\sin z \right)=x\] \[\therefore x.x=\left( 1+\sin x \right)\left( 1-\sin x \right)\left( 1+\sin y \right)\left( 1-\sin y \right)\left( 1+\sin z \right)\left( 1-sinz \right)\] \[=\left( 1-si{{n}^{2}}x \right)\left( 1-si{{n}^{2}}y \right)\left( 1-si{{n}^{2}}z \right)\] \[=co{{s}^{2}}x.co{{s}^{2}}y.co{{s}^{2}}z\] \[\therefore x=\pm \text{ }cosx.cosy.cosz\]
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