If the range of f ( θ ) = s i n 4 θ + c o s 2 θ s i n 4 θ + 3 c o s 2 θ , θ ∈ R is [ α , β ] , then the sum of the infinite G.P., whose first term is 64 and the common ratio is β α , is equal to__

Question

If the range of f ( θ ) = s i n 4 θ + c o s 2 θ s i n 4 θ + 3 c o s 2 θ ​ , θ ∈ R is [ α , β ] , then the sum of the infinite G.P., whose first term is 64 and the common ratio is β α ​ , is equal to________

TestHub · Accepted Answer

​ f ( θ ) = sin 4 θ + cos 2 θ sin 4 θ + 3 cos 2 θ ​ f ( θ ) = 1 + sin 4 θ + cos 2 θ 2 cos 2 θ ​ f ( θ ) = cos 4 θ − cos 2 θ + 1 2 cos 2 θ ​ + 1 f ( θ ) = cos 2 θ + sec 2 θ − 1 2 ​ + 1 f ( θ ) ∣ min. ​ = 1 f ( θ ) max. ​ = 3 S = 1 − 1/3 64 ​ = 96 ​

Mathematics - Functions Question with Solution | TestHub

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