Question

If $A$ and $B$ are non-zero complementary angles, then the point whose cordinates are $(\sin B+\cos A,\tan B+\cot A)$ lies in

• A. First quadrant only
• B. Second quadrant only
• C. Both first and second quadrant
• D. Third quadrant only

Answer 1

The correct option is A First quadrant only

As $A$ and $B$ are non zero complementary angles, so
$A+B={90}^{\circ }A,B\ne 0^{\circ }\Rightarrow 0^{\circ }<A<{90}^{\circ },0^{\circ }<B<{90}^{\circ }$

Now,
$(\sin B+\cos A,\tan B+\cot A)=\left(\sin \right({90}^{\circ }-A)+\cos A,\tan ({90}^{\circ }-A)+\cot A)=(\cos A+\cos A,\cot A+\cot A)=(2\cos A,2\cot A)$

As $0^{\circ }<A<{90}^{\circ }$, so
$\cos A,\cot A>0$
Hence, the coordinate lies in first quadrant.