What is the general solution for sin(x)+cos(x)=tan(x)+1 ?

The general solution for sin(x)+cos(x)=tan(x)+1 is x=2pin,x=(3pi)/4+pin

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sin(x)+cos(x)=tan(x)+1

sin (x) + cos (x) = tan (x) + 1

x = 2 πn, x = \frac{3 π}{4} + πn

Solution steps

sin (x) + cos (x) = tan (x) + 1

Subtract

tan (x) + 1

from both sides

sin (x) + cos (x) - tan (x) - 1 = 0

Express with sin, cos

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

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

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

Factor

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

(cos (x) - 1) (sin (x) + cos (x)) = 0

Solving each part separately

cos (x) - 1 = 0 or sin (x) + cos (x) = 0

cos (x) - 1 = 0 : x = 2 πn

sin (x) + cos (x) = 0 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = 2 πn, x = \frac{3 π}{4} + πn

cos (x) = \frac{1}{4}, 0 \leq x \leq 2 π

tan^{2} (x) + 1 = a^{2}

2 = 2 cos (t)

50 sin (4 5^{\circ}) = 600 sin (θ)

a, tan (a \cdot x^{0.5}) = - x^{0.5}

What is the general solution for sin(x)+cos(x)=tan(x)+1 ?
The general solution for sin(x)+cos(x)=tan(x)+1 is x=2pin,x=(3pi)/4+pin