What is the value of tan((pi/2)/2)-csc(pi/2) ?

The value of tan((pi/2)/2)-csc(pi/2) is 0

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tan((pi/2)/2)-csc(pi/2)

tan (\frac{\frac{π}{2}}{2}) - csc (\frac{π}{2})

0

Solution steps

tan (\frac{\frac{π}{2}}{2}) - csc (\frac{π}{2})

Rewrite using trig identities:

tan (\frac{\frac{π}{2}}{2}) = 1

tan (\frac{\frac{π}{2}}{2})

Simplify:

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

= tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 1

Use the following trivial identity:

csc (\frac{π}{2}) = 1

csc (\frac{π}{2})

csc (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 1

= 1 - 1

Simplify

= 0

\frac{2}{3 \cdot ( 0.2285 6 ^{2} ) \cdot sin ( 6 0 ^{\circ} )}

tan^{2} (5 9^{\circ})

5 sin^{2} (\frac{3 π}{2}) + 3 cos^{2} (4 π) - 7 tan (\frac{π}{4})

sin^{2} (6 5^{\circ})

cos (6 0^{\circ}) sin (3 0^{\circ})

What is the value of tan((pi/2)/2)-csc(pi/2) ?
The value of tan((pi/2)/2)-csc(pi/2) is 0