What is the general solution for -e^{-sin(x)}(sin(x)+cos^2(x))=0 ?

The general solution for -e^{-sin(x)}(sin(x)+cos^2(x))=0 is x=-0.66623…+2pin,x=pi+0.66623…+2pin

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-e^{-sin(x)}(sin(x)+cos^2(x))=0

- e^{- s i n (x)} (sin (x) + cos^{2} (x)) = 0

x = - 0.66623 \dots + 2 πn, x = π + 0.66623 \dots + 2 πn

Solution steps

- e^{- s i n (x)} (sin (x) + cos^{2} (x)) = 0

Rewrite using trig identities

- (1 + sin (x) - sin^{2} (x)) e^{- s i n (x)} = 0

Solve by substitution

sin (x) = - \frac{- 1 + 5}{2}, sin (x) = \frac{1 + 5}{2}

sin (x) = - \frac{- 1 + 5}{2} : x = arcsin (- \frac{- 1 + 5}{2}) + 2 πn, x = π + arcsin (\frac{- 1 + 5}{2}) + 2 πn

sin (x) = \frac{1 + 5}{2} :

No Solution

Combine all the solutions

x = arcsin (- \frac{- 1 + 5}{2}) + 2 πn, x = π + arcsin (\frac{- 1 + 5}{2}) + 2 πn

Show solutions in decimal form

x = - 0.66623 \dots + 2 πn, x = π + 0.66623 \dots + 2 πn

cos^{2} (β) - cot^{2} (β) = cos^{2} (β) cot^{2} (β)

4 tan (x) + 4 = 0, 0 \leq x < 2 π

cos^{3} (x) = cos (x), 0 \leq x < 2 π

3 - 2 sin^{2} (x) = 2 sin^{2} (\frac{x}{2})

cot (θ) = - \frac{7}{5}, \frac{3 π}{2} < θ < 2 π, tan (θ)

What is the general solution for -e^{-sin(x)}(sin(x)+cos^2(x))=0 ?
The general solution for -e^{-sin(x)}(sin(x)+cos^2(x))=0 is x=-0.66623…+2pin,x=pi+0.66623…+2pin