InterviewSolution
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InterviewSolution
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उदाहरण 5. सिद्ध कीजिएह 2 Ix अंडा 5sin—sin —sin —sin— = —5 5 5 5 16 |
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Answer» If A + B =π, then⇒ A =π - B⇒ sin A = sin(π-B)= sin A = sin B∴π/5 + 4π/5 =π⇒ sinπ/5 = sin 4π/5 and 2π/5 + 3π/5 =π⇒ sin 2π/5 = sin 3π/5∴L.H.S. = sinπ/5 sin 2π/5 sin 3π/5 sin 4π/5= L.H.S. = sinπ/5 sin 2π/5 sin 2π/5 sinπ/5⇒ L.H.S. = (sinπ/5 sin 2π/5)² = (sin 36° sin 72°)² = (sin 36° sin 18°)²⇒L.H.S.= {(√10-2√5/4)× (√10+2√5/4)}² = (10-2√5/16)× 10+2√5/16⇒L.H.S = 100-20/256= 80/256= 5/16 = R.H.S.L.H.S. = R.H.S. hence proved |
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