What is the general solution for 2sin^{23}(x)+sin^{26}(x)-2=0 ?

The general solution for 2sin^{23}(x)+sin^{26}(x)-2=0 is x=1.38743…+2pin,x=pi-1.38743…+2pin

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2sin^{23}(x)+sin^{26}(x)-2=0

2 sin^{23} (x) + sin^{26} (x) - 2 = 0

x = 1.38743 \dots + 2 πn, x = π - 1.38743 \dots + 2 πn

Solution steps

2 sin^{23} (x) + sin^{26} (x) - 2 = 0

Rewrite using trig identities

- 2 + \frac{1}{csc ^{26} ( x )} + \frac{2}{csc ^{23} ( x )} = 0

Solve by substitution

csc (x) \approx 1.01704 \dots, csc (x) \approx - 0.79244 \dots

csc (x) = 1.01704 \dots : x = arccsc (1.01704 \dots) + 2 πn, x = π - arccsc (1.01704 \dots) + 2 πn

csc (x) = - 0.79244 \dots :

No Solution

Combine all the solutions

x = arccsc (1.01704 \dots) + 2 πn, x = π - arccsc (1.01704 \dots) + 2 πn

Show solutions in decimal form

x = 1.38743 \dots + 2 πn, x = π - 1.38743 \dots + 2 πn

arccos (3 x) = 1

sin (θ) - cos (θ) = \frac{3}{2}, θ [\frac{3 π}{2}, 2 π]

1 6^{s i n (x)} = 8^{c s c (x)}

tan^{2} (x) - 6 tan (x) - 7 = 0

3 sin (2 x) = 2, 0 \leq x \leq π

What is the general solution for 2sin^{23}(x)+sin^{26}(x)-2=0 ?
The general solution for 2sin^{23}(x)+sin^{26}(x)-2=0 is x=1.38743…+2pin,x=pi-1.38743…+2pin