Question

If tan 3x = sin45° cos 45 ° + sin 30° , find the value of x​

Answer 1

Answer: mark branliest

Step-by-step explanation:

tan3x=sin45∘cos45∘+sin30∘  

⟹tan3x=12–√⋅12–√+12

⟹tan3x=12+12

⟹tan3x=1=tanπ4

⟹3x=nπ+π4,n∈Z

∵ The general solution of tanx=tany is x=nπ+y,n∈Z

⟹x=nπ3+π12,n∈Z

Answer 2

Answer:   15º

Step-by-step explanation:

Given: tan 3x = sin 45º cos 45º + sin 30°.

To find:  Value of x

Previous Knowledge:  

Very important basic trigonometry values

$\begin{tabular}{| c | c | c | c | c | c |}\cline{ 1-6 }\multicolumn{6}{| c |}{Trigonometric Values} \\\cline{ 1-6}Angle&0^{\circ}&30^{\circ}&45^{\circ}&60^{\circ}&90^{\circ}\\\cline{ 1-6 } sin\theta & 0 & 1/2 & 1/\sqrt{2} & 3/\sqrt{2} & 1\\cos\theta & 1 & \sqrt{3}/2 & 1 & 1/2 & 0\\tan\theta & 0 & 1/\sqrt{3} & 1 & \sqrt{3} & nd\\cot\theta& nd & \sqrt{3} & 1 & 1/\sqrt{3} & 0\\sec\theta & 1 & 2/\sqrt{3} & \sqrt{2} & 2 & nd\\cosec\theta & nd & 2 & \sqrt{2} & 2/\sqrt{3} & 1\\\cline{1-6} \end{tabular}$

 Solution:

⇒ tan 3x =  $\frac{1}{\sqrt{2} }$ ×$\frac{1}{\sqrt{2} }$  +   $\frac{1}{2}$

⇒ tan 3x = $\frac{1}{2}$ +

⇒ tan 3x = 1                        [Since tan 45º = 1 ]

⇒ 3x = 45º

⇒ x = $\frac{45}{3}$ = 15º

Thanks!