Railways Sample Paper RRBs Assistant Loco Pilot and Technician CBT STAGE-I Sample Paper-26

  • question_answer
    If \[\tan \,A=1\] and \[\tan B=\sqrt{3},\] then \[cos\,\,A.cos\,\,B.sin\,\,A\,\,sin\,\,B\] is equal to

    A)  \[\frac{1+\sqrt{3}}{2\sqrt{2}}\]

    B)  \[\frac{1-\sqrt{3}}{2\sqrt{2}}\]

    C)  \[\frac{2\sqrt{2}}{3}\]  

    D)  1

    Correct Answer: B

    Solution :

    \[\because \]\[\tan A=1=\tan \frac{\pi }{4}\Rightarrow A=\frac{\pi }{4}\] and \[\tan B\sqrt{3}=\tan \frac{\pi }{3}\Rightarrow B=\frac{\pi }{3}\] \[\therefore \]\[\cos A.\cos \,\,B-sin\,\,A.sin\,\,B\] \[=cos\frac{\pi }{4}.\cos \frac{\pi }{3}-\sin \frac{\pi }{4}\sin \frac{\pi }{3}\] \[=\frac{1}{\sqrt{2}}\cdot \frac{1}{2}-\frac{1}{\sqrt{2}}\frac{\sqrt{3}}{2}=\frac{1-\sqrt{3}}{2\sqrt{2}}\]

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