If the range of f ( )= sin^4 ⁡ +3 cos^2 ⁡ sin^4 ⁡ + cos^2 ⁡ , ∈R is [ , ], then the sum of the infinite G.P., whose first term is 64 and the common ratio is , is equal to_______

Question

Accepted Answer

Correct answer: 96. (96) f ( )= sin^4 ⁡ +3 cos^2 ⁡ sin^4 ⁡ + cos^2 ⁡ f ( )=1+ 2 cos^2 ⁡ sin^4 ⁡ + cos^2 ⁡ f ( )= 2 cos^2 ⁡ cos^4 ⁡ - cos^2 ⁡ +1+1f ( )= 2 cos^2 ⁡ + sec^2 ⁡ -1+1 (f ( ) )_ min .=1f ( )_ max .=3S= 641-1/3=96

$If the range of f (θ) = \frac{sin ^{4} θ + 3 cos ^{2} θ}{sin ^{4} θ + cos ^{2} θ}, θ \in R is [α, β], then the sum of the infinite G.P., whose first term is 64 and the common ratio is \frac{α}{β}, is equal to_______$

Solution

More Sets, Relations & Functions PYQs