Question

No of roots of equation cos^7-sin^4=1 that lies in interval. 0,2π

Answer 1

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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