8cosec^2a +25sin^2a=?
Answers
Given : 8cosec²a +25sin²a
To Find : Least Value
Solution:
z = 8cosec²a +25sin²a
dz/da = 8*2coseca.(-coseca.cota) + 25*2sinacosa
= -16 cosa/sin³a + 50sinacosa
put dz/da = 0
=> -16 cosa/sin³a + 50sinacosa = 0
=> 16 cosa/sin³a = 50sinacosa
=> 16 cosa = 50sin⁴acosa
=> 8cosa = 25sin⁴acosa
=> 8 = 25sin⁴a
=> 8 - 25sin⁴a = 0
=> sin⁴a = 8/25
=> sin²a = 2√2 /5
sin²a = 2√2 /5 => cosec²a = 1 = 5/2√2
z = 8cosec²a +25sin²a = 8 * 5/2√2 + 25 * 2√2 /5
= 10√2 + 10√2
= 20√2
20√2 is the least Value
Learn More:Find the least value of number of terms of series 20,18,16, for which ...
https://brainly.in/question/19295575
If tan, cot & are roots of x² + 2ax + b = 0, then least value of
https://brainly.in/question/20795953
Find the least value of n for which the sum of the series 20+28+36+ ...
https://brainly.in/question/11092057