What is the general solution for 2cos^2(x)+3sin^2(x)=2 ?

The general solution for 2cos^2(x)+3sin^2(x)=2 is x=2pin,x=pi+2pin

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2cos^2(x)+3sin^2(x)=2

2 cos^{2} (x) + 3 sin^{2} (x) = 2

x = 2 πn, x = π + 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

2 cos^{2} (x) + 3 sin^{2} (x) = 2

Subtract

2

from both sides

2 cos^{2} (x) + 3 sin^{2} (x) - 2 = 0

Rewrite using trig identities

- 2 + 2 cos^{2} (x) + 3 sin^{2} (x)

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

cos^{2} (x) = 1 - sin^{2} (x)

= - 2 + 2 (1 - sin^{2} (x)) + 3 sin^{2} (x)

Simplify

- 2 + 2 (1 - sin^{2} (x)) + 3 sin^{2} (x) : sin^{2} (x)

- 2 + 2 (1 - sin^{2} (x)) + 3 sin^{2} (x)

Expand

2 (1 - sin^{2} (x)) : 2 - 2 sin^{2} (x)

2 (1 - sin^{2} (x))

Apply the distributive law:

a (b - c) = ab - a c

a = 2, b = 1, c = sin^{2} (x)

= 2 \cdot 1 - 2 sin^{2} (x)

Multiply the numbers:

2 \cdot 1 = 2

= 2 - 2 sin^{2} (x)

= - 2 + 2 - 2 sin^{2} (x) + 3 sin^{2} (x)

Simplify

- 2 + 2 - 2 sin^{2} (x) + 3 sin^{2} (x) : sin^{2} (x)

- 2 + 2 - 2 sin^{2} (x) + 3 sin^{2} (x)

Add similar elements:

- 2 sin^{2} (x) + 3 sin^{2} (x) = sin^{2} (x)

= - 2 + 2 + sin^{2} (x)

- 2 + 2 = 0

= sin^{2} (x)

= sin^{2} (x)

= sin^{2} (x)

sin^{2} (x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

sin (x) = 0

General solutions for

sin (x) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

42 - 25 cos (x) = 31

2 sec^{2} (x) = 5 tan (x)

cos^{2} (2 x) - 3 sin^{2} (x) - 1 = 0

sin (- t) = \frac{3}{10}

cos^{2} (x) + sin^{3} (x) = 0

What is the general solution for 2cos^2(x)+3sin^2(x)=2 ?
The general solution for 2cos^2(x)+3sin^2(x)=2 is x=2pin,x=pi+2pin