If 5 sec theta ndash 3 tan theta 5 then what is the value of 5 tan theta ndash 3 sec theta ........

Quantitative Aptitude (CGL) Trignometry

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If 5 sec θ – 3 tan θ = 5, then what is the value of 5 tan θ – 3 sec θ?

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Explanation:

GIVEN: 5 sec A - 3tan A = 5
=> 5 √(tan² A +1) = 5 + 3 tanA
=> 25( tan² A + 1) = 25 + 9 tan² A + 30 tanA
=> 25 tan² A - 9tan² A = 30 tanA=> 16 tan² A - 30 tanA = 0
=> 2tanA ( 8 tanA - 15 ) = 0
=> tanA = 0 or tanA = 15/8 …………. (1)
If tan A = 0 ………….. (1)
5 sec A - 3 tan A = 5
=> 5sec A -3 * 0 = 5
=> sec A = 1 ………… (1)’
If tan A = 15/8 ……… (2)
5sec A - 3* 15/8 = 5
=> 5 sec A = 5 + 45/8
=> 5 secA = 85 /8
=> sec A = 17/8 ………… (2)’
So, 5 tanA - 3 sec A = 5 * 0 - 3* 1 = -3
Or, 5*15/8 - 3*17/8 = 75/8 - 51/8 = 24/8 = 3