SOLUTION: 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)

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).

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
How to prove
1.

start with right side
...........use identity
=.........simplify
=
=

2.

start with right side
.........use identity

=

=

=

=

3.

start with left side
.........use identities and
=....use again
=
=
=

4.

start with left side
.....use identity
=
= ....use identity
=
=
=
=
=

5.

start with left side
....use identity
=
=
=....factor out
=
=
=

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