What is the general solution for sin(a)cos(a)=1 ?

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

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sin(a)cos(a)=1

sin (a) cos (a) = 1

No Solution for a \in R

Solution steps

sin (a) cos (a) = 1

Rewrite using trig identities

sin (a) cos (a)

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 a )}{2}

\frac{sin ( 2 a )}{2} = 1

Multiply both sides by

2

\frac{sin ( 2 a )}{2} = 1

Multiply both sides by

2

\frac{2 sin ( 2 a )}{2} = 1 \cdot 2

Simplify

sin (2 a) = 2

sin (2 a) = 2

- 1 \leq sin (x) \leq 1

No Solution for a \in R

sin (2 π x) = 0

sin (5 x) = 1

tan (θ) = 2.2

8 sin (θ) - 43 = 0

0 = 1 + 2 cos (x)

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