What is the general solution for sin(5X)*cos(5X)=1 ?

The general solution for sin(5X)*cos(5X)=1 is No Solution for X\in\mathbb{R}

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sin(5X)*cos(5X)=1

sin (5 X) \cdot cos (5 X) = 1

No Solution for X \in R

Solution steps

sin (5 X) cos (5 X) = 1

Rewrite using trig identities

sin (5 X) cos (5 X)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

= \frac{sin ( 2 \cdot 5 X )}{2}

\frac{sin ( 2 \cdot 5 X )}{2} = 1

Multiply both sides by

2

\frac{sin ( 2 \cdot 5 X )}{2} = 1

Multiply both sides by

2

\frac{2 sin ( 2 \cdot 5 X )}{2} = 1 \cdot 2

Simplify

sin (2 \cdot 5 X) = 2

sin (2 \cdot 5 X) = 2

- 1 \leq sin (x) \leq 1

No Solution for X \in R

100 + 60 sin (\frac{7 π}{3} x) = 100

sin^{2} (a) = 3 cos^{2} (a)

3 cot (x) + 3 = 0

3 cos (x) + \frac{9}{2} = 5 + 4 cos (x)

sec (2 x) + 2 = 0

What is the general solution for sin(5X)*cos(5X)=1 ?
The general solution for sin(5X)*cos(5X)=1 is No Solution for X\in\mathbb{R}