What is the general solution for csc(3θ)=sec(15) ?

The general solution for csc(3θ)=sec(15) is θ=(1.30899…)/3+(360n)/3 ,θ=60-(1.30899…)/3+(360n)/3

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csc(3θ)=sec(15)

csc (3 θ) = sec (1 5^{\circ})

θ = \frac{1.30899 \dots}{3} + \frac{36 0 ^{\circ} n}{3}, θ = 6 0^{\circ} - \frac{1.30899 \dots}{3} + \frac{36 0 ^{\circ} n}{3}

Solution steps

csc (3 θ) = sec (1 5^{\circ})

sec (1 5^{\circ}) = 6 - 2

csc (3 θ) = 6 - 2

Apply trig inverse properties

3 θ = arccsc (6 - 2) + 36 0^{\circ} n, 3 θ = 18 0^{\circ} - arccsc (6 - 2) + 36 0^{\circ} n

Solve

3 θ = arccsc (6 - 2) + 36 0^{\circ} n : θ = \frac{arccsc ( 6 - 2 )}{3} + \frac{36 0 ^{\circ} n}{3}

Solve

3 θ = 18 0^{\circ} - arccsc (6 - 2) + 36 0^{\circ} n : θ = 6 0^{\circ} - \frac{arccsc ( 6 - 2 )}{3} + \frac{36 0 ^{\circ} n}{3}

θ = \frac{arccsc ( 6 - 2 )}{3} + \frac{36 0 ^{\circ} n}{3}, θ = 6 0^{\circ} - \frac{arccsc ( 6 - 2 )}{3} + \frac{36 0 ^{\circ} n}{3}

Show solutions in decimal form

θ = \frac{1.30899 \dots}{3} + \frac{36 0 ^{\circ} n}{3}, θ = 6 0^{\circ} - \frac{1.30899 \dots}{3} + \frac{36 0 ^{\circ} n}{3}

2 cot^{2} (x) + tan (x) = cot (x)

sin (2 x) = sin (\frac{π}{2} - x)

tan (X) = 1

2 sec^{2} (x) - sec (x) - 1 = 0

4 tan (4 θ) = 4

What is the general solution for csc(3θ)=sec(15) ?
The general solution for csc(3θ)=sec(15) is θ=(1.30899…)/3+(360n)/3 ,θ=60-(1.30899…)/3+(360n)/3