SSC Sample Paper Mock Test-20 SSC CGL Tear-II Paper-1

For any quadrilateral ABCD which of the following statements are true?                    I. \[\sin \,(A+B)+\sin \,(C+D)=0\]                 II. \[\cos \,(A+B)=\cos \,(C+D)\]

A)              Only I

B) Only II

C) Both I and II

D) None of these

Correct Answer: B

Solution :

As,\[A+B+C+D=360{}^\circ \]

\[\therefore \] \[A+B=360{}^\circ -\,\,(C+D)\]

\[\therefore \]\[\sin \,\,(A+B)=\sin \,\,[360{}^\circ -\,\,(C+D)]=-\sin \,\,(C+D)\]

\[\therefore \]\[\sin \,\,(A+B)+\sin \,\,(C+D)=0\]

Also, \[\cos \,\,(A+B)=cos\,\,[360{}^\circ -(C+D)]\]

\[\cos \,(A+B)=\cos \,\,(C+D)\]