Expert: Ahmed Salami - 3/15/2010

Question
Prove                  cos^2x+cot^2xcos^2x=cot^2x.
I solved till cos^2x+(cos^2x)/(tan^2x)=cot^2x

is there an identity to solve further? thanks

Answer
Hi Joseph,
From the identity:
sin˛x + cos˛x = 1
dividing through by sin˛x, we have
sin˛x/sin˛x + cos˛x/sin˛x = 1/sin˛x
1 + cot˛x = cosec˛x

Now,
cos˛x + cot˛x.cos˛x = cos˛x(1 + cot˛x)
                   = cos˛x(cosec˛x)
                   = cos˛x/sin˛x
                   = cot˛x

Regards