What is the general solution for cos(105)cos(x)=-1/4 ?

The general solution for cos(105)cos(x)=-1/4 is No Solution for x\in\mathbb{R}

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cos(105)cos(x)=-1/4

cos (10 5^{\circ}) cos (x^{\circ}) = - \frac{1}{4}

No Solution for x \in R

Solution steps

cos (10 5^{\circ}) cos (x^{\circ}) = - \frac{1}{4}

cos (10 5^{\circ}) = \frac{2 ( 1 - 3 )}{4}

\frac{2 ( 1 - 3 )}{4} cos (x^{\circ}) = - \frac{1}{4}

Multiply both sides by

4

2 (1 - 3) cos (x^{\circ}) = - 1

Divide both sides by

2 (1 - 3)

cos (x^{\circ}) = \frac{2 ( 1 + 3 )}{4}

Apply trig inverse properties

x^{\circ} = arccos (\frac{2 ( 1 + 3 )}{4}) + 36 0^{\circ} n, x^{\circ} = 36 0^{\circ} - arccos (\frac{2 ( 1 + 3 )}{4}) + 36 0^{\circ} n

No Solution for x \in R

cos (θ) tan^{2} (θ) = 3 cos (θ)

cos (θ) = 0.56

cos (θ) = 0.17

sin (2 x) - 3 cos (x) = 0

5 cos (x) + 1 = 1

What is the general solution for cos(105)cos(x)=-1/4 ?
The general solution for cos(105)cos(x)=-1/4 is No Solution for x\in\mathbb{R}