Question

if tan theta ,2 tan theta+2,3 tan theta are in GP.then the value of 7-5cot theta/9-4underroot sec square theta -1 is
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Answer 1

Answer:

33/-28

Step-by-step explanation:

Given,

tanθ, 2tanθ + 2, 3tanθ + 3 are in G.P

⇒ (2tanθ + 2)² = tanθ(3 tanθ + 3)

⇒ 4 tan²θ + 4 + 8 tanθ = 3 tan²θ +  3 tanθ

⇒ tan²θ + 5 tanθ + 4 = 0

⇒ tan²θ + tanθ + 4 tanθ + 4 = 0

⇒ (tanθ  + 1)(tanθ + 4 = 0)

⇒ tanθ = -4 {∵ -1 wont be satisfied}

So,

tanθ = -4

Then,

cotθ = -1/4

sec²θ = 1 + tan²θ = √17

Now,

(7 - 5 cotθ)/(9 - 4√sec²θ - 1)

⇒ (7 - 5 * -1/4)/9 - 4(4))

=> (28 + 5)/4(-7)

⇒ 33/-28

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