Question
Download Solution PDFयदि \(tan40^0 = \alpha\) है, तो \(\frac{tan320^0 - tan 310^0}{1 + tan320^0.tan 310^0}\) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
tan 40° = α
प्रयुक्त सूत्र:
Tan (A - B) = (tan A - tan B)/1 + tan A × tan B
tan (90° - θ) = cot θ
cot θ × tan θ = 1
गणना:
⇒ \(\frac{tan320^0 - tan 310^0}{1 + tan320^0.tan 310^0}\) = tan (320° - 310°)
⇒ tan 10°
अब, हम लिख सकते हैं:
Tan 10° = tan (50° - 40°)
⇒ [(tan 50° - tan 40°)/1 + (tan 50° × tan 40°)]
⇒ [tan (90° - 40°) - tan 40°/1 + tan (90° - 40°) × tan 40°]
⇒ cot 40° - tan 40°/ 1 + cot 40° × tan 40°
⇒ (1/α - α)/1 + 1
⇒ (1/α - α)/2
⇒ (1 - α2)/2α
∴ सही उत्तर (1 - α2)/2α है।
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