What is the general solution for arctan(4x)+arctan(6x)=90 ?

The general solution for arctan(4x)+arctan(6x)=90 is No Solution for x\in\mathbb{R}

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arctan(4x)+arctan(6x)=90

arctan (4 x) + arctan (6 x) = 90

No Solution for x \in R

Solution steps

arctan (4 x) + arctan (6 x) = 90

Rewrite using trig identities

arctan (4 x) + arctan (6 x)

Use the Sum to Product identity:

arctan (s) + arctan (t) = arctan (\frac{s + t}{1 - s t})

= arctan (\frac{4 x + 6 x}{1 - 4 x \cdot 6 x})

arctan (\frac{4 x + 6 x}{1 - 4 x \cdot 6 x}) = 90

- \frac{π}{2} < arctan (x) < \frac{π}{2}

No Solution

Verify solutions by plugging them into the original equation

Check the solutions by plugging them into

arctan (4 x) + arctan (6 x) = 90

Remove the ones that don't agree with the equation.

No Solution for x \in R

2 sin (θ) tan (θ) - tan (θ) = 1 - 2 sin (θ)

7 cos (2 θ) - 9 = - 9 sin (θ)

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

tan (a) = \frac{8}{5}

2 cos^{2} (x) - 7 cos (x) + 3 = 0, (0, 2 π)

What is the general solution for arctan(4x)+arctan(6x)=90 ?
The general solution for arctan(4x)+arctan(6x)=90 is No Solution for x\in\mathbb{R}