Question
Download Solution PDFयदि tan 48° tan 23° tan 42° tan 67° = tan(A + 30∘) तो A होगा
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त सूत्र:
tan(90° - θ) = cot θ
tan θ × cot θ = 1
गणना:
दिया गया है कि,
tan 48° tan 23° tan 42° tan 67° = tan(A + 30∘)
⇒ tan (90° - 42°)tan(90 - 67°)tan 42°tan 67° = tan(A + 30°)
⇒ cot 42° cot 67° tan 42°tan 67° = tan(A + 30°)
∵ tan θ × cot θ = 1
⇒ 1 × 1 = tan(A + 30°)
⇒ tan 45° = tan(A + 30°) (∵ tan 45° = 1)
⇒ 45° = A + 30°
⇒ A = 15°
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