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Popular >

solvefor x,sin(x^e)+cos(y^e)=1

Solution

solve for

x, sin (x^{e}) + cos (y^{e}) = 1

Solution

x = (arcsin (1 - cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}, x = (π + arcsin (- 1 + cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

Solution steps

sin (x^{e}) + cos (y^{e}) = 1

Move

cos (y^{e})

to the right side

sin (x^{e}) + cos (y^{e}) = 1

Subtract

cos (y^{e})

from both sides

sin (x^{e}) + cos (y^{e}) - cos (y^{e}) = 1 - cos (y^{e})

Simplify

sin (x^{e}) = 1 - cos (y^{e})

sin (x^{e}) = 1 - cos (y^{e})

Apply trig inverse properties

sin (x^{e}) = 1 - cos (y^{e})

General solutions for

sin (x^{e}) = 1 - cos (y^{e})

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x^{e} = arcsin (1 - cos (y^{e})) + 2 πn, x^{e} = π + arcsin (- 1 + cos (y^{e})) + 2 πn

x^{e} = arcsin (1 - cos (y^{e})) + 2 πn, x^{e} = π + arcsin (- 1 + cos (y^{e})) + 2 πn

Solve

x^{e} = arcsin (1 - cos (y^{e})) + 2 πn : x = (arcsin (1 - cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

x^{e} = arcsin (1 - cos (y^{e})) + 2 πn

Take both sides of the equation to the power of

\frac{9545}{25946} : x = (arcsin (1 - cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

x^{e} = arcsin (1 - cos (y^{e})) + 2 πn

(x^{e})^{\frac{9545}{25946}} = (arcsin (1 - cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

x = (arcsin (1 - cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

x = (arcsin (1 - cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

Solve

x^{e} = π + arcsin (- 1 + cos (y^{e})) + 2 πn : x = (π + arcsin (- 1 + cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

x^{e} = π + arcsin (- 1 + cos (y^{e})) + 2 πn

Take both sides of the equation to the power of

\frac{9545}{25946} : x = (π + arcsin (- 1 + cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

x^{e} = π + arcsin (- 1 + cos (y^{e})) + 2 πn

(x^{e})^{\frac{9545}{25946}} = (π + arcsin (- 1 + cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

x = (π + arcsin (- 1 + cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

x = (π + arcsin (- 1 + cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

x = (arcsin (1 - cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}, x = (π + arcsin (- 1 + cos (y^{e})) + 2 πn)^{\frac{9545}{25946}}

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