What is the general solution for tan(x)= 3/(10cos(x)),0<x<90 ?

The general solution for tan(x)= 3/(10cos(x)),0<x<90 is x=0.30469…

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tan(x)= 3/(10cos(x)),0<x<90

tan (x) = \frac{3}{10 cos ( x )}, 0^{\circ} < x < 9 0^{\circ}

x = 0.30469 \dots

Solution steps

tan (x) = \frac{3}{10 cos ( x )}, 0^{\circ} < x < 9 0^{\circ}

Subtract

\frac{3}{10 cos ( x )}

from both sides

tan (x) - \frac{3}{10 cos ( x )} = 0

Simplify

tan (x) - \frac{3}{10 cos ( x )} : \frac{10 tan ( x ) cos ( x ) - 3}{10 cos ( x )}

\frac{10 tan ( x ) cos ( x ) - 3}{10 cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

10 tan (x) cos (x) - 3 = 0

Rewrite using trig identities

- 3 + 10 sin (x) = 0

Move

3

to the right side

10 sin (x) = 3

Divide both sides by

10

sin (x) = \frac{3}{10}

Apply trig inverse properties

x = arcsin (\frac{3}{10}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{10}) + 36 0^{\circ} n

Solutions for the range

0 < x < 9 0^{\circ}

x = arcsin (\frac{3}{10})

Show solutions in decimal form

x = 0.30469 \dots

2 cos^{2} (x) - 3 cos (x) = 0, 0, 2 π

2 cos^{2} (x) - 5 sin (x) = 4

2 cos (2 θ) - 7 cos (θ) + 2 = - 4 cos (θ)

sin (5 x - 15) = sin (5 \cdot x)

3 cos (x) - 1 = 4 cos (x)

What is the general solution for tan(x)= 3/(10cos(x)),0<x<90 ?
The general solution for tan(x)= 3/(10cos(x)),0<x<90 is x=0.30469…