Question
Download Solution PDFIf 1 + sin2 θ + sin4 θ + ... upto ∞ = 2, then θ = ______
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The sum of an infinite G.P. is
S = \(\rm a\over 1-r\)
Where a is the first term of the series and r is the common ratio
Calculation:
Given: 1 + sin2 θ + sin4 θ + ....∞ = 2
a = 1, r = sin2 θ
⇒ \(\rm {1\over 1\ -\ sin^2\ θ} = 2\) (∵ 1 - sin2 θ = cos2 θ)
⇒ \(\rm {1\over{cos^2\ {θ}}} = 2\)
⇒ sec2 θ = 2
⇒ sec θ = √2
Then θ = 45°
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