Question -
Answer -
Let △ABC inwhich ∠B=90°
We know that, cot function is the reciprocalof tan function and it is written as
cot(A) = AB/BC = 4/3
Let AB = 4k an BC =3k, where k is a positivereal number.
According to the Pythagorean theorem,
AC2=AB2+BC2
AC2=(4k)2+(3k)2
AC2=16k2+9k2
AC2=25k2
AC=5k
Now, apply the values corresponding to theratios
tan(A) = BC/AB = 3/4
sin (A) = BC/AC = 3/5
cos (A) = AB/AC = 4/5
Now compare the left hand side(LHS) with righthand side(RHS)
Since, both the LHS and RHS = 7/25
R.H.S. =L.H.S.
Hence, (1-tan2 A)/(1+tan2 A) = cos2 A– sin 2 A is proved