Trigonometry Practice Test 1

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Question : 27 of 40

Marks: +1, -0

If

\sec√{2+√{2+√{2+...∞}}},

what is the value of

\cos θ(1+2\cos θ)?

0
-1
1
2
None of these

Solution:

Let

x=√{2+√{2 ...∞}}

⇒x^2=2+x

⇒x^2-x-2=0

⇒(x-1)(x+1)=0

⇒x=2

∴\sec θ=2=2\sec π/3

⇒θ=π/3

Now

\cosθ(1+2\cosθ)

=\cosπ/3(1+2\cosπ/3)

=1/2(1+2 × 1/2)=2/2=1

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