What is the general solution for 2sin(15)cos(15)=tan(x) ?

The general solution for 2sin(15)cos(15)=tan(x) is x=0.46364…+180n

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2sin(15)cos(15)=tan(x)

2 sin (1 5^{\circ}) cos (1 5^{\circ}) = tan (x)

x = 0.46364 \dots + 18 0^{\circ} n

Solution steps

2 sin (1 5^{\circ}) cos (1 5^{\circ}) = tan (x)

sin (1 5^{\circ}) = \frac{6 - 2}{4}

cos (1 5^{\circ}) = \frac{6 + 2}{4}

2 \cdot \frac{6 - 2}{4} \cdot \frac{6 + 2}{4} = tan (x)

Switch sides

tan (x) = 2 \cdot \frac{6 - 2}{4} \cdot \frac{6 + 2}{4}

Simplify

2 \cdot \frac{6 - 2}{4} \cdot \frac{6 + 2}{4} : \frac{1}{2}

Apply trig inverse properties

x = arctan (\frac{1}{2}) + 18 0^{\circ} n

Show solutions in decimal form

x = 0.46364 \dots + 18 0^{\circ} n

6 sin^{2} (x) + 5 cos (x) = 7

3 cos (x) + sin (x) = - 1

- 3 = tan^{2} (θ) - 2 - 2 tan (θ)

- 2 cos^{2} (x) - 9 sin (x) - 3 = 0

sin (2 x) = - \frac{2 6}{7}

What is the general solution for 2sin(15)cos(15)=tan(x) ?
The general solution for 2sin(15)cos(15)=tan(x) is x=0.46364…+180n