What is the general solution for sin(45+a)cos(45+a)=(sqrt(2))/2 ?

The general solution for sin(45+a)cos(45+a)=(sqrt(2))/2 is No Solution for a\in\mathbb{R}

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sin(45+a)cos(45+a)=(sqrt(2))/2

sin (4 5^{\circ} + a) cos (4 5^{\circ} + a) = \frac{2}{2}

No Solution for a \in R

Solution steps

sin (4 5^{\circ} + a) cos (4 5^{\circ} + a) = \frac{2}{2}

Rewrite using trig identities

sin (4 5^{\circ} + a) cos (4 5^{\circ} + 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 ( 4 5 ^{\circ} + a ) )}{2}

\frac{sin ( 2 ( 4 5 ^{\circ} + a ) )}{2} = \frac{2}{2}

Multiply both sides by

2

\frac{sin ( 2 ( 4 5 ^{\circ} + a ) )}{2} = \frac{2}{2}

Multiply both sides by

2

\frac{2 sin ( 2 ( 4 5 ^{\circ} + a ) )}{2} = \frac{2 2}{2}

Simplify

sin (2 (4 5^{\circ} + a)) = 2

sin (2 (4 5^{\circ} + a)) = 2

- 1 \leq sin (x) \leq 1

No Solution for a \in R

tan (x) \cdot sin (x) = 5219

sin (z) = 2

2 \cdot sin^{2} (x) + sin (x) = 1

sin (x) = \frac{9}{10}

4 sin (x) - sec (x) = 0

What is the general solution for sin(45+a)cos(45+a)=(sqrt(2))/2 ?
The general solution for sin(45+a)cos(45+a)=(sqrt(2))/2 is No Solution for a\in\mathbb{R}