Solution
Solution
+1
Decimal Notation
Solution steps
Rewrite using trig identities:
Rewrite as
Use the following trivial identity: Use the following trivial identity:
Use the Angle Sum identity:
Simplify:
Least Common Multiplier of
Least Common Multiplier (LCM)
Prime factorization of
divides by
divides by
Prime factorization of
divides by
Multiply each factor the greatest number of times it occurs in either or
Multiply the numbers:
Adjust Fractions based on the LCM
Multiply each numerator by the same amount needed to multiply its
corresponding denominator to turn it into the LCM
For multiply the denominator and numerator by
Since the denominators are equal, combine the fractions:
Add similar elements:
Apply exponent rule:
Apply radical rule:
Apply exponent rule:
Multiply fractions:
Cancel the common factor:
Rewrite using trig identities:
Rewrite using trig identities:
Write as
Use the Half Angle identity:
Use the Double Angle identity
Substitute with
Switch sides
Divide both sides by
Square root both sides
Choose the root sign according to the quadrant of :
Use the following trivial identity:
periodicity table with cycle:
Simplify
Apply rule
Join
Convert element to fraction:
Since the denominators are equal, combine the fractions:
Multiply the numbers:
Apply the fraction rule:
Multiply the numbers:
Apply radical rule: assuming
Factor the number:
Apply radical rule:
Simplify
Apply exponent rule:
Apply radical rule:
Apply exponent rule:
Multiply fractions:
Cancel the common factor:
Multiply fractions:
Cancel the common factor:
Popular Examples
Frequently Asked Questions (FAQ)
What is the value of (sin(pi/8)+cos(pi/8))^2 ?
The value of (sin(pi/8)+cos(pi/8))^2 is (2+sqrt(2))/2