if sin^2a-cos^2a = tan^b then prove that cos^2b - sin^2b= cot^2a

Question

If sin^2a-cos^2a = tan^b then prove that cos^2b - sin^2b= cot^2a high school maths 

Answer 1

If Mr. Alan is correct. We have:

Cos^2b = 1/(tan^2b + 1)

Sin^2b = tan^2b/(1+tan^2b)

Then, Cos^2b - Sin^2b = (1 - tan^2b)/(1+tan^2b) (1)

By assuming that the input statement is: sin^2a - cos^2a = tan^2b (the original could have a typing error)

The expression (1) is:

Cos^2b - Sin^2b = (1 - sin^2a + cos^2a)/(1 + sin^2a - cos^2a) But sin^2a + cos^2a = 1

Cos^2b - Sin^2b = (1 - (1-cos^2a) + cos^2a)/(1 + sin^2a - (1-sin^2a))

Cos^2b - Sin^2b = 2 cos^2a/ 2 sin^2a = 1/cot^2a

Answer 2

Ab,

 

I am making some assumptions about your question as I post this answer. First, it looks like you meant to send

 

sin² a − cos² a = tan b, 

 

ans asked to prove that 

 

cos² b − sin² b = cot² a.

Before I send any more, do you know anything more about a or b?

 

Please verify that my assumptions are true or false, and correct them if need be.

 

Thank you.