What is the general solution for cos(pi/2+x)+sin(pi/2+x)=0 ?

The general solution for cos(pi/2+x)+sin(pi/2+x)=0 is x=2pin-(3pi)/4 ,x=pi+2pin-(3pi)/4

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cos(pi/2+x)+sin(pi/2+x)=0

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

x = 2 πn - \frac{3 π}{4}, x = π + 2 πn - \frac{3 π}{4}

Solution steps

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

Rewrite using trig identities

2 sin (\frac{π}{2} + x + \frac{π}{4}) = 0

Divide both sides by

2

sin (\frac{π}{2} + x + \frac{π}{4}) = 0

General solutions for

sin (\frac{π}{2} + x + \frac{π}{4}) = 0

\frac{π}{2} + x + \frac{π}{4} = 0 + 2 πn, \frac{π}{2} + x + \frac{π}{4} = π + 2 πn

Solve

\frac{π}{2} + x + \frac{π}{4} = 0 + 2 πn : x = 2 πn - \frac{3 π}{4}

Solve

\frac{π}{2} + x + \frac{π}{4} = π + 2 πn : x = π + 2 πn - \frac{3 π}{4}

x = 2 πn - \frac{3 π}{4}, x = π + 2 πn - \frac{3 π}{4}

10 tan (b) + 12 = tan (b) + 6

arctan (x) + arctan (1 - x) = arctan (\frac{4}{3})

cos (θ) = \frac{- 8}{14 \cdot 20}

sin^{2} (x) = \frac{1}{3}

cot (x) = \frac{2}{3}

What is the general solution for cos(pi/2+x)+sin(pi/2+x)=0 ?
The general solution for cos(pi/2+x)+sin(pi/2+x)=0 is x=2pin-(3pi)/4 ,x=pi+2pin-(3pi)/4