Question

If tan 6, 2 tan 8 + 2, 3 tan 0 + 3 are in G.P. then the
7--5 cot
value of
is equal to
9-4V sec2 0-1​

Answer 1

Answer:

-33/28

Step-by-step explanation:

According to the question we know that if the terms of a GP are a,b,c, then

a^2=bc,

⇒ (2tanθ+2)  ^2  =(3tanθ+3)tanθ,

4(tan θ)^2+8tanθ+4=3(tanθ)^2+3tanθ,

(tanθ)^2+5tanθ+4=0

So tanθ = -1 or -4, but -1 does satisfy the GP condition,

Therefore tanθ=-4

We know that cotθ=1/tanθ and also

(secθ)^2-1=(tanθ)^2,

By substituting we get,

7+1.25/9-16,

⇒8.25/-7,        (By multiplying by 4)

-33/28

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