Question 1170774: How to prove
1.sinθ = cosθ tanθ
2. 1/cosθ=tanθ/sinθ
3. cos2 θ tan2 θ = sin2 θ
4. sinθtanθ + cosθ =1/cosθ
5. sinθ(1 + tanθ) = tanθ(sinθ + cosθ) Found 2 solutions by math_helper, MathLover1:Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website! 1.sin(θ) = cos(θ) tan(θ)
Start with tan(θ) = sin(θ)/cos(θ), then multiply both sides by cos(θ)
2. 1/cos(θ)=tan(θ)/sin(θ)
Start with tan(θ) = sin(θ)/cos(θ), then divide both sides by sin(θ)
3.
Starting with
tan(θ) = sin(θ)/cos(θ)
we get:
Next just multiply both sides by
4. sin(θ)tan(θ) + cos(θ) = 1/cos(θ)
Using
tan(θ) = sin(θ)/cos(θ)
Re-write LHS of given equation (#4) as
= sin(θ)*sin(θ)/cos(θ) + cos(θ)
Put both terms over cos(θ):
=
=
Noting that :
=
I leave #5 for you to do, there are enough examples here. As a hint: start with the LHS, multiply thru by sin(θ) then factor out tan(θ).
