Question
Download Solution PDF(sin4 45°+ cos4 60°) + (tan4 45°+ cot4 45°) का मान है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया है:
(sin4 45°+ cos4 60°) + (tan4 45°+ cot4 45°)
प्रयुक्त अवधारणा:
sin 45° = \(\frac{1}{\sqrt{2}}\), cos 60° = \(\frac{1}{2}\), tan 45° = 1, cot 45° = 1
गणन:
⇒ प्रश्न के अनुसार,
⇒ (sin4 45°+ cos4 60°) + (tan4 45°+ cot4 45°)
⇒ उपरोक्त समीकरण में कोणों का मान रखने पर,
⇒ (\(\frac{1}{\sqrt{2}}\))4 + (\(\frac{1}{2}\))4 + (1 + 1) = \(\frac{1}{4}\) + \(\frac{1}{16}\) + 2
⇒ \(\frac{4+1+2\times16}{16}\) = \(\frac{4+1+32}{16}\) = \(\frac{37}{16}\)
अतः, (sin4 45°+ cos4 60°) + (tan4 45°+ cot4 45°) का मान \(\frac{37}{16}\) है।
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