What is the general solution for sinh(z)=0 ?

The general solution for sinh(z)=0 is z=0

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sinh(z)=0

sinh (z) = 0

z = 0

Degrees

z = 0^{\circ}

Solution steps

sinh (z) = 0

Rewrite using trig identities

sinh (z) = 0

Use the Hyperbolic identity:

sinh (x) = \frac{e ^{x} - e ^{- x}}{2}

\frac{e ^{z} - e ^{- z}}{2} = 0

\frac{e ^{z} - e ^{- z}}{2} = 0

\frac{e ^{z} - e ^{- z}}{2} = 0 : z = 0

\frac{e ^{z} - e ^{- z}}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

e^{z} - e^{- z} = 0

Add

e^{- z}

to both sides

e^{z} - e^{- z} + e^{- z} = 0 + e^{- z}

Simplify

e^{z} = e^{- z}

Apply exponent rules

e^{z} = e^{- z}

a^{f (x)} = a^{g (x)}

, then

f (x) = g (x)

z = - z

z = - z

Solve

z = - z : z = 0

z = - z

Move

z

to the left side

z = - z

Add

z

to both sides

z + z = - z + z

Simplify

2 z = 0

2 z = 0

Divide both sides by

2

2 z = 0

Divide both sides by

2

\frac{2 z}{2} = \frac{0}{2}

Simplify

z = 0

z = 0

z = 0

z = 0

\frac{1}{cos ( θ )} = 2 cos (θ)

2 sin (x) tan (x) + 5 tan (x) = 0

tan (3 x) = 3, 0 \leq x \leq 2 π

sin (3 x) cos (x) = - cos (3 x) sin (x)

6 sin^{2} (x) + sin (x) - 1 = 0

What is the general solution for sinh(z)=0 ?
The general solution for sinh(z)=0 is z=0