a)cos^2 alfa - sin^2 alfa = 1 +2sin^2 alfa

b)cos^2 alfa - sin^2 alfa =2cos^2 alfa - 1

c)1+tan^2 alfa = 1/sin^2 alfa

e)1+tan^2 alfa /tan^2 alfa = 1/sin^2 alfa

help!(Headbang)

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- Mar 26th 2010, 10:33 AMlebanonestablish the following:
a)cos^2 alfa - sin^2 alfa = 1 +2sin^2 alfa

b)cos^2 alfa - sin^2 alfa =2cos^2 alfa - 1

c)1+tan^2 alfa = 1/sin^2 alfa

e)1+tan^2 alfa /tan^2 alfa = 1/sin^2 alfa

help!(Headbang) - Mar 26th 2010, 12:12 PMGrandad
Hello lebanonYou have one or two mistakes in these equations, which I'll point out as we come to them. They are all based on the fundamental relationship between sine and cosine:

...(1)which is the trigonometric form of Pythagoras' Theorem.

From this we can deduce:...(2)and:...(3)So in (a), we start with the LHS and use (2) to eliminate :

(Note the minus sign.)

, because

, again using the fact that , so .