Find the Exact Value sec(pi/12)

Math
Split into two angles where the values of the six trigonometric functions are known.
Apply the difference of angles identity.
The exact value of is .
The exact value of is .
The exact value of is .
The exact value of is .
The exact value of is .
The exact value of is .
The exact value of is .
The exact value of is .
Simplify .
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Multiply and .
Combine and .
Combine and .
Simplify the denominator.
Tap for more steps…
Move to the left of .
Multiply by .
Combine and simplify the denominator.
Tap for more steps…
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Tap for more steps…
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Divide by .
Evaluate the exponent.
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Rewrite the expression.
Combine and .
Combine and .
Multiply by .
Combine and simplify the denominator.
Tap for more steps…
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Tap for more steps…
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Divide by .
Evaluate the exponent.
Simplify the numerator.
Tap for more steps…
Combine using the product rule for radicals.
Multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps…
Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply by .
Simplify the numerator.
Tap for more steps…
Multiply by .
Multiply by .
Simplify the denominator.
Tap for more steps…
Combine using the product rule for radicals.
Multiply by .
Simplify the numerator.
Tap for more steps…
Combine and into a single radical.
Cancel the common factor of and .
Tap for more steps…
Factor out of .
Cancel the common factors.
Tap for more steps…
Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite as .
Any root of is .
Multiply by .
Combine and simplify the denominator.
Tap for more steps…
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Tap for more steps…
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Divide by .
Evaluate the exponent.
Combine and .
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Rewrite the expression.
Combine and .
Combine and .
Cancel the common factor of and .
Tap for more steps…
Factor out of .
Cancel the common factors.
Tap for more steps…
Factor out of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Multiply and .
Expand the denominator using the FOIL method.
Simplify.
Cancel the common factor of and .
Tap for more steps…
Factor out of .
Cancel the common factors.
Tap for more steps…
Factor out of .
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply .
Tap for more steps…
Combine using the product rule for radicals.
Multiply by .
Multiply .
Tap for more steps…
Combine using the product rule for radicals.
Multiply by .
Simplify each term.
Tap for more steps…
Rewrite as .
Tap for more steps…
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Cancel the common factor of and .
Tap for more steps…
Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
Tap for more steps…
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Find the Exact Value sec(pi/12)

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top