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
Hello lebanon...(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 :
In (b) we do the same, but eliminating using (3):(Note the minus sign.)
In (c) there's another mistake: the RHS should be . This time, we start with (1) and divide both sides by :
Finally, for part (e) (I wonder what happened to (d)?) we take the result in part (c) and divide both sides by :
, again using the fact that , so .