Question

if cosA = 2/5 find 4 +4tansquareA

Answer 1

cosA = 2/5 = b/h
h^2 = b^2+p^2
5^2 = 2^2+p^2
25 = 4 +p^2        
p^2 = 21
p = root of 21
                      =  4+4tan^2A
                      =  4 + 4*21/4
                      = 4+21
                      = 25 

Answer 2

Cos A=base/hypotenuse =2/5

Then hypotenuse =5x, base=2x

By Pythagoras theorem

25x²-4x²=hieght²

21x²=hieght²

√21x²=hieght

Tan²A=hieght²/base² =21x²/4x²=21/4

4+4*21/4 =4+21=25

25 is your answer