Originally Posted by

**BeckyDWood** Please help with any of the following..

Prove these identities

cos2x = (1 - tan^2 x)/(1 +tan^2 x)

note that 1 + tan^2 x = sec^2 x

cos2x = cos^4 x - sin^4 x

factor the right side

cosec2x + cot2x = cot x

left side ...

1/sin(2x) + cos(2x)/sin(2x)

[1 + cos(2x)]/sin(2x)

now use cos(2x) = 2cos^2 x - 1 and sin(2x) = 2sinxcosx

sin2x = 2tanx / (1 + tan^2 x)

same hint as the first

tan x = sqrt ((1 - cos2x) / (1 + cos2x))

on the right side, try these substitutions ...

numerator ... cos(2x) = 1 - 2sin^2 x

denominator ... cos(2x) = 2cos^2 x - 1