Question
Download Solution PDF\(cot 18^{\circ}\left(\cot 72^{\circ} \cdot \cos^2 22^{\circ} + \frac{1}{\tan 72^{\circ} \cdot \sec^2 68^{\circ}}\right)\) இன் மதிப்பைக் கண்டறியவும்.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFசூத்திரம்:
- cot A = 1/ tan A
- cos A = 1/ sec A
- sin A = cos (90° - A)
- cos2 A + sin2 A = 1
-
tan A = cot (90° - A)
கணக்கீடு:
\(cot 18^{\circ}\left(\cot 72^{\circ} \cdot \cos^2 22^{\circ} + \frac{1}{\tan 72^{\circ} \cdot \sec^2 68^{\circ}}\right)\)
⇒ cot 18° (cot 72° . cos2 22° + cot 72° . cos2 68°) (∵ cot A = 1/ tan A மற்றும் cos A = 1/ sec A)
⇒ cot 18° [cot 72° (cos2 22° + cos2 68°)]
⇒ cot 18° . cot 72° (cos2 22° + sin2 22°) [∵ sin A = cos (90° - A)]
⇒ cot 18° . cot 72° (∵ cos2 A + sin2 A = 1)
⇒ cot 18° . tan 18° [∵ tan A = cot (90° - A)]
⇒ 1
எனவே, \(cot 18^{\circ}\left(\cot 72^{\circ} \cdot \cos^2 22^{\circ} + \frac{1}{\tan 72^{\circ} \cdot \sec^2 68^{\circ}}\right)\)= 1.
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