If Cotθ = 3/√(5), 0o < θ < 90o, then the value of (6Sec2θ - 5/3Cosec2θ)/(3/5Sec2θ + 4/3Cosec2θ) , is equal to:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 1.
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Understanding/Application |
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Cotθ = 3/√(5) tanθ = √(5)/3 sec2θ = 1 + tan2θ = 1 + (√5/3)2 = 14/9 cosec2θ = 1 + Cot2θ = 1 + (3/√(5))2 = 14/5 |
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(6Sec2θ - 5(Cosec2θ)/3)/(3(Sec2θ)/5 + 4(Cosec2θ)/3) = [6(14/9) - 5(14)/3(5)]/[3(14)/5(9) + 4(14)/3(5) = (28/3 - 14/3)/(14/15 + 56/15) = 14(15)/3(70) = 1 |