# Verify the Identity (tan(x))/(1-tan(x)^2)=(sin(x)cos(x))/(2cos(x)^2-1)

Verify the Identity (tan(x))/(1-tan(x)^2)=(sin(x)cos(x))/(2cos(x)^2-1)
Start on the left side.
Apply Pythagorean identity in reverse.
Convert to sines and cosines.
Write in sines and cosines using the quotient identity.
Apply the reciprocal identity to .
Apply the product rule to .
Simplify.
Multiply the numerator by the reciprocal of the denominator.
One to any power is one.
Simplify the denominator.
Apply the distributive property.
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine the numerators over the common denominator.
Combine.
Multiply by .
Combine and .
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply the numerator by the reciprocal of the denominator.
Combine and .
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
Write as a fraction with denominator .
Combine.
Remove parentheses.
Multiply by .
Move the negative in front of the fraction.
Rewrite as .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
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### Name

Name four hundred thirty million seven hundred ninety thousand four hundred

### Interesting facts

• 430790400 has 4096 divisors, whose sum is 15554713824
• The reverse of 430790400 is 004097034
• Previous prime number is 81

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 27
• Digital Root 9

### Name

Name one billion six hundred seventy million nine hundred sixty-one thousand eight hundred fifty-six

### Interesting facts

• 1670961856 has 256 divisors, whose sum is 19047312000
• The reverse of 1670961856 is 6581690761
• Previous prime number is 1471

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 49
• Digital Root 4

### Name

Name one billion five hundred seventy-one million five hundred fifty thousand seven hundred eighty-one

### Interesting facts

• 1571550781 has 8 divisors, whose sum is 1663407200
• The reverse of 1571550781 is 1870551751
• Previous prime number is 181

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 40
• Digital Root 4