Home > Trigonometry > Proving Identities

How do you write #cos^2 0.45-sin^2 0.45# as a single trigonometric function?

Answer 1

Nolan Alexander

#cos 0.9#

Use the formula: #cos 2 theta = cos^2 theta -sin^2 theta#

#cos^2 0.45-sin^2 0.45#

#=cos 2(0.45)#

#=cos 0.9#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Abigail Armstrong

To write ( \cos^2(0.45) - \sin^2(0.45) ) as a single trigonometric function, you can use the Pythagorean identity ( \cos^2(x) = 1 - \sin^2(x) ) for any angle ( x ).

Substituting ( 0.45 ) into the Pythagorean identity:

[ \cos^2(0.45) = 1 - \sin^2(0.45) ]

So, ( \cos^2(0.45) - \sin^2(0.45) ) becomes:

[ 1 - \sin^2(0.45) - \sin^2(0.45) ]

[ = 1 - 2\sin^2(0.45) ]

Therefore, ( \cos^2(0.45) - \sin^2(0.45) ) can be written as ( 1 - 2\sin^2(0.45) ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.