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\sin(x)-\cos(x)=0

Algebra Calculus Trigonometry Matrix

Question

\sin\left(x\right)-\cos\left(x\right)=0

Solve the equation

x=\frac{\pi }{4}+k\pi ,k \in \mathbb{Z}

Alternative Form

x=45^{\circ}+180^{\circ} k,k \in \mathbb{Z}

Alternative Form

x\approx 0.785398+k\pi ,k \in \mathbb{Z}

Evaluate

\sin\left(x\right)-\cos\left(x\right)=0

Move the expression to the right side

-\cos\left(x\right)=0-\sin\left(x\right)

Subtract the terms

-\cos\left(x\right)=-\sin\left(x\right)

Divide both sides

\frac{-\cos\left(x\right)}{\sin\left(x\right)}=-1

Divide the terms

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Evaluate

\frac{-\cos\left(x\right)}{\sin\left(x\right)}

\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}

-\frac{\cos\left(x\right)}{\sin\left(x\right)}

Rewrite the expression

-\sin^{-1}\left(x\right)\cos\left(x\right)

Rewrite the expression

-\cot\left(x\right)

-\cot\left(x\right)=-1

\text{Multiply both sides of the equation by }-1

-\cot\left(x\right)\left(-1\right)=-\left(-1\right)

Calculate

\cot\left(x\right)=-\left(-1\right)

Multiplying or dividing an even number of negative terms equals a positive

\cot\left(x\right)=1

Use the inverse trigonometric function

x=\operatorname{arccot}\left(1\right)

Calculate

x=\frac{\pi }{4}

Solution

x=\frac{\pi }{4}+k\pi ,k \in \mathbb{Z}

Alternative Form

x=45^{\circ}+180^{\circ} k,k \in \mathbb{Z}

Alternative Form

x\approx 0.785398+k\pi ,k \in \mathbb{Z}

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