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Popular >

1/(cos^2(pi))

Solution

\frac{1}{cos ^{2} ( π )}

Solution

1

Solution steps

\frac{1}{cos ^{2} ( π )}

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

= \frac{1}{( - 1 ) ^{2}}

Simplify

\frac{1}{( - 1 ) ^{2}} : 1

\frac{1}{( - 1 ) ^{2}}

(- 1)^{2} = 1

(- 1)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

if

n

is even

(- 1)^{2} = 1^{2}

= 1^{2}

Apply rule

1^{a} = 1

= 1

= \frac{1}{1}

Apply rule

\frac{a}{1} = a

= 1

= 1

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Frequently Asked Questions (FAQ)

What is the value of 1/(cos^2(pi)) ?
The value of 1/(cos^2(pi)) is 1