MCQ
If $A$ and $B$ are complementary angles, then:
- A$\sin\text{A}=\sin\text{B}$
- B$\cos\text{A}=\cos\text{B}$
- C$\tan\text{A}=\tan\text{B}$
- ✓$\sec\text{A}=\text{cosec B}$
✓
Answer
Correct option: D.
$\sec\text{A}=\text{cosec B}$
Given: $A$ and are $B$ are complementary angles
Since $\sec(90^\circ-\text{B})=\text{cosec }\text{B}$
therefore $A + B = 90^\circ$
$\Rightarrow\text{A}=90^\circ-\text{B}$
$\Rightarrow\sec\text{A}=\sec(90^\circ-\text{B})$
$\Rightarrow\sec\text{A}=\text{cosec }\text{B}$
Hence the correct option is $(d)$
Since $\sec(90^\circ-\text{B})=\text{cosec }\text{B}$
therefore $A + B = 90^\circ$
$\Rightarrow\text{A}=90^\circ-\text{B}$
$\Rightarrow\sec\text{A}=\sec(90^\circ-\text{B})$
$\Rightarrow\sec\text{A}=\text{cosec }\text{B}$
Hence the correct option is $(d)$
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A. 65°
B. 130°
C. 295°
D. 230°