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

The general solution for (cos(x))/(csc(x))+(sin(x))/(sec(x))=1 is x= pi/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(cos(x))/(csc(x))+(sin(x))/(sec(x))=1

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

x = \frac{π}{4} + πn

Solution steps

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

Subtract

1

from both sides

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

Simplify

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

\frac{cos ( x ) sec ( x ) + sin ( x ) csc ( x ) - csc ( x ) sec ( x )}{csc ( x ) sec ( x )} = 0

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

cos (x) sec (x) + sin (x) csc (x) - csc (x) sec (x) = 0

Express with sin, cos

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

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

- 1 + 2 cos (x) sin (x) = 0

Rewrite using trig identities

- 1 + sin (2 x) = 0

Move

1

to the right side

sin (2 x) = 1

General solutions for

sin (2 x) = 1

2 x = \frac{π}{2} + 2 πn

Solve

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

x = \frac{π}{4} + πn

cot (θ) = - 8

t, 0 = (1.8) cos (2 π f t)

2 cot (x) cos (x) + 2 cos (x) = cot (x) + 1

tan (θ) - 7 = - 12 cot (θ)

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

What is the general solution for (cos(x))/(csc(x))+(sin(x))/(sec(x))=1 ?
The general solution for (cos(x))/(csc(x))+(sin(x))/(sec(x))=1 is x= pi/4+pin