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Popular >

cos(x)=1-sin^2(x/2)

Solution

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

Solution

x = 4 πn, x = 2 π + 4 πn

+1

Solution steps

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

Subtract

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

from both sides

cos (x) - 1 + sin^{2} (\frac{x}{2}) = 0

Rewrite using trig identities

- 1 + cos^{2} (\frac{x}{2}) = 0

Solve by substitution

cos (\frac{x}{2}) = 1, cos (\frac{x}{2}) = - 1

cos (\frac{x}{2}) = 1 : x = 4 πn

cos (\frac{x}{2}) = - 1 : x = 2 π + 4 πn

Combine all the solutions

x = 4 πn, x = 2 π + 4 πn

Popular Examples

3sin(x)-4sin^3(x)=1-2sin^2(x)

3 sin (x) - 4 sin^{3} (x) = 1 - 2 sin^{2} (x)

sin^2(a)=((2tan(a)))/((1+tan^2(a)))

sin^{2} (a) = \frac{( 2 tan ( a ) )}{( 1 + tan ^{2} ( a ) )}

(tan(a))/2 = 2/11

\frac{tan ( a )}{2} = \frac{2}{11}

sin^2(x)-cos(x)= 1/2

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

cos(x)[3sin(x)-2]=0

cos (x) [3 sin (x) - 2] = 0

Frequently Asked Questions (FAQ)

What is the general solution for cos(x)=1-sin^2(x/2) ?
The general solution for cos(x)=1-sin^2(x/2) is x=4pin,x=2pi+4pin