Verify the Identity csc(x)^4-csc(x)^2=cot(x)^4+cot(x)^2

Verify the Identity csc(x)^4-csc(x)^2=cot(x)^4+cot(x)^2
Start on the right side.
Factor out of .
Tap for more steps...
Factor out of .
Multiply by .
Factor out of .
Apply Pythagorean identity.
Tap for more steps...
Rearrange terms.
Apply pythagorean identity.
Apply Pythagorean identity in reverse.
Convert to sines and cosines.
Tap for more steps...
Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the product rule to .
Apply the product rule to .
Simplify.
Tap for more steps...
One to any power is one.
One to any power is one.
Apply the distributive property.
Multiply .
Tap for more steps...
Multiply and .
Multiply by by adding the exponents.
Tap for more steps...
Use the power rule to combine exponents.
Add and .
Rewrite as .
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 by adding the exponents.
Tap for more steps...
Use the power rule to combine exponents.
Add and .
Combine the numerators over the common denominator.
Simplify the numerator.
Now consider the left side of the equation.
Convert to sines and cosines.
Tap for more steps...
Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the product rule to .
Apply the product rule to .
Simplify.
Tap for more steps...
Simplify each term.
Tap for more steps...
One to any power is one.
One to any power is one.
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 by adding the exponents.
Tap for more steps...
Use the power rule to combine exponents.
Add and .
Combine the numerators over the common denominator.
Simplify the numerator.
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Do you know how to Verify the Identity csc(x)^4-csc(x)^2=cot(x)^4+cot(x)^2? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.