AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\frac{1}{\sin 3^{\circ} \sin 4^{\circ}}+\ldots+\frac{1}{\sin 89^{\circ} \sin 90^{\circ}}=\)
- A \(\frac{\sin 1^{\circ}}{\tan 1^{\circ}}\)
- B \(\frac{1}{\sin ^2 1^{\circ}}\)
- C \(\frac{\cot 1^{\circ}}{\sin 1^{\circ}}\)
- D \(\frac{\tan 1^{\circ}}{\cos 1^{\circ}}\)
Answer & Solution
Correct Answer
(C) \(\frac{\cot 1^{\circ}}{\sin 1^{\circ}}\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{\sin 1^{\circ}} \sum_{n=1}^{89} \frac{\sin((n+1)-n)^{\circ}}{\sin n^{\circ} \sin (n+1)^{\circ}}\) \(\frac{1}{\sin 1^{\circ}} \sum_{n=1}^{89} (\cot n^{\circ} - \cot(n+1)^{\circ})\) \(\frac{1}{\sin 1^{\circ}} (\cot 1^{\circ} - \cot 90^{\circ})\)…
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