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4sin-cosB+1& 30 ९ - ८०४४०...If4 tvm 0 = 3, evaluate 4sin®+cos0-1 ) |
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Answer» Let theta = A4tanA=3tanA = 3/4 = P/B In a ∆ ABC right angled at B.Base (AB) = 4 , Perpendicular( BC) = 3 AC² = AB² + BC²[By Pythagoras theorem]AC² = 4² + 3²AC² = 16 + 9 = 25AC= √25 = 5 The trigonometric ratios sin A = P/H = 3/5Cos A = B/H = 4/54sinA-cosA+1)/4sinA+cosA-1= (4×3/5 -4/5 +1) /(4×3/5 + 4/5 -1)= 12/5 - (4+5)/5 / 12/5 + (4 -5/5)= (12/5 +1/5) / (12/5 -1/5)= 13/5 / 11/5= 13/5 × 5/11 = 13/11 (4sinA-cosA+1)/(4sinA+cosA-1) = 13/11. |
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