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If, cos∅ + cos²∅ = 1 Then, find sin⁸∅ + 2Sin⁶∅ + sin⁴∅?Explain with steps please! |
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Answer» ong>Answer: heyy unaku antha aasif ku ennachu Step-by-step EXPLANATION: Given → cos∅ + cos²∅ = 1
→ cos∅ + 1 - sin²∅ = 1
→ cos∅ = sin²∅
Solution → sin¹²∅ + 3SIN^(10)∅ + 3 sin^8∅ + sin^6∅ + 2sin⁴∅ + 2 sin²∅ - 2 = 1
→ (sin⁴∅)³ + 3 (sin⁴∅)² (sin²∅) + 3 sin⁴∅(sin²∅)² + (sin²∅)³ + 2(sin²∅)² + 2 sin²∅ - 2 = 1
→ (sin⁴∅ + sin²∅)³ 2(sin²∅)² + 2 sin²∅ - 2 = 1
→ [(sin²∅)² + sin²∅]³ + 2(sin²∅)² + 2 sin²∅ - 2 = 1
→ (cos²∅ + cos∅)³ + 2(cos²∅ + cos∅) - 2 = 1
Since cos²∅ + cos∅ = 1
→ 1³ + 2(1) - 2 = 1
→ 1 = 1
→ L.H.S = R.H.S
Hence Proved |
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