A) 3
B) 2
C) \[\frac{3}{2}\]
D) 1
Correct Answer: D
Solution :
In \[\Delta \,ABC,\] \[A+B+C=\pi \] or \[\frac{\pi }{2}+B+C=\pi \] or \[B+C=\frac{\pi }{2}\] or \[C=\frac{\pi }{2}-B\] \[\therefore \] \[{{\cos }^{2}}A+{{\cos }^{2}}B+{{\cos }^{2}}C\] \[={{\cos }^{2}}\frac{\pi }{2}+{{\cos }^{2}}B+{{\cos }^{2}}\left( \frac{\pi }{2}-B \right)\] \[=0+({{\cos }^{2}}B+{{\sin }^{2}}B)=1\]You need to login to perform this action.
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