What is the general solution for (sin(x)+cos(x))^2=(1+2sin(x))/(sec(x)) ?

The general solution for (sin(x)+cos(x))^2=(1+2sin(x))/(sec(x)) is x=2pin

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(sin(x)+cos(x))^2=(1+2sin(x))/(sec(x))

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

x = 2 πn

Solution steps

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

Subtract

\frac{1 + 2 sin ( x )}{sec ( x )}

from both sides

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

Simplify

(sin (x) + cos (x))^{2} - \frac{1 + 2 sin ( x )}{sec ( x )} : \frac{sin ^{2} ( x ) sec ( x ) + 2 sec ( x ) sin ( x ) cos ( x ) + cos ^{2} ( x ) sec ( x ) - 1 - 2 sin ( x )}{sec ( x )}

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Express with sin, cos

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

- cos (x) + 1 = 0

Move

1

to the right side

- cos (x) = - 1

Divide both sides by

- 1

cos (x) = 1

General solutions for

cos (x) = 1

x = 0 + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn

cot (\frac{π}{3}) = tan (x)

3 cot (x) + 1 = 2 + 4 cot (x), 0^{\circ} \leq x \leq 36 0^{\circ}

sin (x) = \frac{48.35}{50.14}

2 tan (\frac{π x}{2}) = sec (\frac{π x}{2})

1.47 = (\frac{sin ( \frac{x + 60}{2} )}{sin ( 3 0 ^{\circ} )})

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