Question:
If \(\text{cosec}(\alpha) = \sec(38^\circ)\), what is the value of \(\alpha\)?
यदि \(\text{cosec}(\alpha) = \sec(38^\circ)\) है, तो \(\alpha\) का मान क्या है?
Options:
- 38°
- 42°
- 48°
- 52°
- 38°
- 42°
- 48°
- 52°
Correct Answer: d)
Explanation:
Using the complementary angle identity \(\sec(\theta) = \text{cosec}(90^\circ – \theta)\):
\(\text{cosec}(\alpha) = \text{cosec}(90^\circ – 38^\circ) = \text{cosec}(52^\circ)\)
\(\alpha = 52^\circ\).
पूरक कोण सूत्र \(\sec(38^\circ) = \text{cosec}(90^\circ – 38^\circ) = \text{cosec}(52^\circ)\) से:
\(\alpha = 52^\circ\)।