Question

1+cosx+cos^2x+cos^3x....to infinity=2+√2 then x equals​

Answer 1

The value of x is 45°

Step-by-step explanation:

The given series is

1 + cosx + cos²x + cos³x + ...∞ = 2 + √2

The left hand side is a GP series, whose first term is 1 and the common ratio is cosx. Then the sum of the series

= 1/(1 - cosx)

Given, 1/(1 - cosx) = 2 + √2

or, 1 - cosx = 1/(2 + √2)

or, 1 - cosx = (2 - √2)/{(2 + √2)(2 - √2)}

or, 1 - cosx = (2 - √2)/(4 - 2)

or, 1 - cosx = (2 - √2)/2

or, cosx = 1 - (2 - √2)/2

or, cosx = (2 - 2 + √2)/2

or, cosx = √2 / 2

or, cosx = 1/√2

or, cosx = cos45°

or, x = 45°

Therefore, x = 45°

Answer 2

Step-by-step explanation:

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