[AERII]

How do I prove that sin theta*cos theta*tan theta= 1-cos squared theta

[Vi Nguyen]

Hi there, with this question you should remember the trig identity tanθ=sinθ/cosθ and cos squaredθ plus sin squaredθ=1

so you have: to prove that Left Hand Side=Right hand side

(LHS) sinθcosθtanθ = 1-cos squaredθ (RHS)

(remember tanθ=sinθ/cosθ) so sub in for tan
sinθcosθ(sinθ/cosθ)
(cosθ cancels and your left with)
sin squaredθ

now from the identity cos squaredθ plus sin squaredθ=1, rearranged you'd get sin squaredθ=1-cos squaredθ

so since you've got sin squaredθ on the LHS and the identity says that this is equal to 1-cos squared, this is proof that the LHS=RHS. Hope this is clear enough, trig gets a little complicated to show when typing. ;p