If tan 3x=sin45* cos 45 +sin30 . find the value of x.

We are given the equation:

tan(3x) = sin 45° * cos 45° + sin 30°

Step 1: Evaluate the Trigonometric Values
We know that:

sin 45° = 1/√2
cos 45° = 1/√2
sin 30° = 1/2
Substituting these values:

tan(3x) = (1/√2) * (1/√2) + 1/2
= 1/2 + 1/2
= 1

Step 2: Solve for 3x
We know that:

tan θ = 1 when θ = 45° + kπ (where k is any integer)

So, we set:

3x = 45° + kπ

Step 3: Solve for x
Dividing both sides by 3:

x = (45° + kπ)/3

Step 4: Express in Radians (if needed)
Since 45° = π/4 in radians, we can rewrite the solution as:

x = (π/4 + kπ)/3
= π/12 + kπ/3

Final Answer
x = π/12 + kπ/3, where k is any integer.

Approved