Home > Trigonometry > Proving Identities

How do I prove this trigonometric identity?

#cos^2beta/(1-sinbeta)=1+sinbeta#

Answer 1

Violet Anderson

#cos^2beta/(1-sinbeta)=1+sinbeta#

#color(white)(# Multiply and divide by #1+sinbeta#

#=>(cos^2beta(1+sinbeta))/((1-sinbeta)(1+sinbeta))#

#color(white)(#

#=>(cos^2beta(1+sinbeta))/(1-sin^2beta)#

#color(white)(#

#=>(cancelcos^2beta(1+sinbeta))/cancel(cos^2beta# #color(white)(#

#->1+sinbeta#

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

Answer 2

Jordan Armstrong

To prove a trigonometric identity, you typically manipulate one side of the equation until it matches the other side using various trigonometric identities and properties such as the Pythagorean identities, sum and difference identities, double angle identities, and so on. The specific method depends on the identity you are trying to prove.

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.