How do you prove that (1 - cos2x)/sin2x = tanx?
How do you prove that (1 - cos2x)/sin2x = tanx?
You need to know some identities for sin2x and cos2x:
sin2x = 2sinxcosx
cos2x = 1 - 2((sinx)^2); The "^" means raise to the power; "^2" means "raise to the power 2" or "square".
(1 - cos2x)/sin2x
= (1 - [ 1 - 2((sinx)^2) ] ) / (2sinxcosx)
= 2((sinx)^2) / (2sinxcosx)
= 2sinxsinx / 2sinxcosx
= sinx / cosx
= tan x.
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