Question

please solve it please I need it​

Answer 1

GIVEN:

2 cosθ = √3

(2cosθ + 1)/(2cosθ - 1) = a + b√3

SOLUTION:

2 cosθ = √3 [Given]

==> cosθ = √3/2

==> θ = 30⁰

(2cosθ + 1)/(2cosθ - 1) = a + b√3 [Given]

∵ cosθ = √3/2,

==> [2(√3/2) + 1]/[2(√3/2) - 1] = a + b√3

LHS:-

==> (√3 + 1)/(√3 - 1)

==> (√3 + 1)(√3+1)/(√3 - 1)(√3 + 1)

[By Conjugate Multiplication]

==> (√3 + 1)²/(3 - 1)

==> (3 + 2√3 + 1)/2

==> (4 + 2√3)/2 [Take 2 as common factor]

==> 2(2 + √3)/2

==> 2 + √3

Now, compare this LHS to the RHS, you can see both of them look similar,

==> 2 + √3 = a + b√3

∴ a = 2, b = 1

Answer 2

Answer:

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