What is the general solution for 0.26=(1-sin(x))/(1+sin(x)) ?

The general solution for 0.26=(1-sin(x))/(1+sin(x)) is x=0.62772…+2pin,x=pi-0.62772…+2pin

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0.26=(1-sin(x))/(1+sin(x))

0.26 = \frac{1 - sin ( x )}{1 + sin ( x )}

x = 0.62772 \dots + 2 πn, x = π - 0.62772 \dots + 2 πn

Solution steps

0.26 = \frac{1 - sin ( x )}{1 + sin ( x )}

Switch sides

\frac{1 - sin ( x )}{1 + sin ( x )} = 0.26

Solve by substitution

sin (x) = \frac{37}{63}

sin (x) = \frac{37}{63} : x = arcsin (\frac{37}{63}) + 2 πn, x = π - arcsin (\frac{37}{63}) + 2 πn

Combine all the solutions

x = arcsin (\frac{37}{63}) + 2 πn, x = π - arcsin (\frac{37}{63}) + 2 πn

Show solutions in decimal form

x = 0.62772 \dots + 2 πn, x = π - 0.62772 \dots + 2 πn

sec (x) = - 2, 0 \leq x \leq 2 π

2 tan^{2} (x) = 2

2 cos (t) = 1

cos (x) = \frac{2}{13}

cos (θ) = sec (θ)

What is the general solution for 0.26=(1-sin(x))/(1+sin(x)) ?
The general solution for 0.26=(1-sin(x))/(1+sin(x)) is x=0.62772…+2pin,x=pi-0.62772…+2pin