Question

If 1-cosA=5/13, prove that 25sinA(sinA - cosA)

Answer 1

if 1 - cosA = 5/13

then cosA = 1-5/13 = 12/13

A could be in I or IV
For I:
cosA = 12/13
then sinA = 5/13

25sinA(sinA-cosA_ = 25(5/13)(5/13 - 12/13)
= ...

for IV
cosA = 12/13
then sinA = -5/13

25sinA(sinA - cosA)
= 25(-5/13)(-5/13 - 12/13)
= ....

I will leave the arithmetic up to you