No of roots of equation cos^7-sin^4=1 that lies in interval. 0,2π
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only solution is 0 for Cos⁷θ - Sin⁴θ = 1 that lies in interval. 0,2π
Step-by-step explanation:
Cos⁷θ - Sin⁴θ = 1
=> Cos⁷θ = 1 + Sin⁴θ
as we know That
Sinθ lies between - 1 & 1
=> Sin⁴θ lies between 0 & 1
=> 1 + Sin⁴θ ≥ 1
While Cos⁷θ lies between - 1 & 1
=> Only Possible Solution
is when Sin⁴θ = 0
=> θ = 0 , 2π
Cos⁷θ at θ = 0 = 1
but Cos⁷θ at θ = 2π = -1
=> only solution is 0
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