Question:
If A and B are complementary angles, then
(a) sin A = sin B
(b) cos A = cos B
(c) tan A = tan B
(d) sec A = cosec B
Solution:
Given: $A$ and are $B$ are complementary angles
Since $\sec \left(90^{\circ}-B\right)=\operatorname{cosec} B$
therefore $A+B=90^{\circ}$
$\Rightarrow A=90^{\circ}-B$
$\Rightarrow \sec A=\sec \left(90^{\circ}-B\right)$
$\Rightarrow \sec A=\operatorname{cosec} B$
Hence the correct option is $(d)$