Question

Find the value of x :

tan 3x = sin45°cos45°+sin30° ​

Answer 1

Answer:

Taking R.H.S we get,

1/2 + 1/2 =1 since sin 45^{\circ} = cos 45^{\circ} = 1/\sqrt{2} and sin 30^{\circ} =1/2

Now

tan 3x =1 = tan 45^{\circ}

so x = 15^{\circ}

Hope it helps!

Answer 2

Step-by-step explanation:

$tan3x = \sin(45 ) . \cos(45) + \sin(30 \\ \tan(3x) = \frac{1}{ \sqrt{2} } \times \frac{1}{ \sqrt{2} } + \frac{1}{2 } \\ \tan(3x) = \frac{1}{2} + \frac{1}{2} \\ \tan(3x) \frac{2}{2} \\ \tan(3x) = 1 \\ \tan(3x) = \tan(45) \\ 3x = 45 \\ x = \frac{45}{3} \\ x = 15$