question_answer

The sides of a triangle are\[\sin \alpha ,\text{ }\cos \alpha \]and\[\sqrt{1+\sin \alpha \cos \alpha }\]for some\[0<\alpha <\frac{\pi }{2}\]. Then, the greatest angle of the triangle is

A) \[60{}^\circ \]  

B)                                        \[90{}^\circ \]                   

C)        \[120{}^\circ \]                 

D)        \[150{}^\circ \]

Correct Answer: C

Solution :

If a, b and c are the sides of a triangle and C is a largest angle, then Letthen \[\Rightarrow \,\cos C=-\frac{\sin \alpha \cos \alpha }{2\sin \alpha \cos \alpha }\]