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If 5 secθ – 3 tanθ = 5, then what is the value of 5 tanθ – 3 secθ?1). 12). 23). 34). 4 |
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Answer» 5 sec Θ - 3tan Θ = 5 ⇒ 5 √(tan² Θ + 1) = 5 + 3tanΘ ⇒ 25(tan² Θ + 1) = 25 + 9tan² Θ + 30 tanΘ ⇒ 25 tan² Θ – 9tan² Θ = 30 tanΘ ⇒ 16 tan² Θ - 30 tanΘ = 0 ⇒ 2tanΘ (8 tanΘ – 15) = 0 ⇒ tanΘ = 0 or tanΘ = 15/8 If TAN Θ = 0 5 sec Θ - 3 tan Θ = 5 ⇒ 5SEC Θ – 3 × 0 = 5 ⇒ sec Θ = 1 If tan Θ = 15/8 5sec Θ – 3 × 15/8 = 5 ⇒ 5 sec Θ = 5 + 45/8 ⇒ 5 secΘ = 85 /8 ⇒ sec Θ = 17/8 So, 5 tanΘ – 3 sec Θ = 5 × 0 – 3 × 1 = -3 Or, 5 × 15/8 – 3 × 17/8 = 75/8 - 51/8 = 24/8 = 3 |
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