What is pisec(3x+pi/2)-1 ?

The solution to pisec(3x+pi/2)-1 is -picsc(3x)-1

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simplify pisec(3x+pi/2)-1

simplify

π sec (3 x + \frac{π}{2}) - 1

- π csc (3 x) - 1

Solution steps

π sec (3 x + \frac{π}{2}) - 1

Rewrite using trig identities

= π (- \frac{1}{sin ( 3 x )}) - 1

Simplify

π (- \frac{1}{sin ( 3 x )}) - 1 : - \frac{π}{sin ( 3 x )} - 1

= - \frac{π}{sin ( 3 x )} - 1

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= - π csc (3 x) - 1

tan (arctan (\frac{x}{2}))

sin (\frac{1}{4} π + x)

sin (a) - sin (- a)

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

sin (arctan (\frac{x}{6}))