Posted by yoshi on Sunday, December 16, 2012 at 1:27pm.
PLEASE tell your classmates to use parentheses to clarify the problems!
I think you mean
(tan*cos^2 + sin^2)/sin
= (sin*cos + sin^2)/sin
= sin(cos+sin)/sin
= cos+sin
I think you mean
(1+tan)/(1-tan)
= (1+tan)^2/(1-tan^2)
= (1+2tan+tan^2)/(1-tan^2)
= (sec^2+2tan)/(1-tan^2)
I think you mean
(sin^2 - cos^2)/(tan*sin+cos*tan)
= (sin-cos)(sin+cos)/(tan(sin+cos)
= (sin-cos)/tan
= sin*cot - cos*cot
= cos-cos*cot
always try simple values for counter-examples:
a=0: 1-1 =? 0 -- yes
a=pi: -1+1 =? 0 -- yes
a=pi/4: √2 - 1/√2 =? 1/√2*√2 NO!