Question

Prove that (1+tan 2θ) (1-sin 2θ) (1+sin 2θ) =1.

Answer 1

Answer:

Using the identities:

1

+

tan

2

θ

=

sec

2

θ

1

sec

θ

=

cos

θ

tan

θ

=

sin

θ

cos

θ

sin

2

θ

=

1

−

cos

2

θ

2

cos

2

θ

−

1

=

cos

2

θ

Start:

1

−

tan

2

θ

1

+

tan

2

θ

=

1

−

tan

2

θ

sec

2

θ

=

Split the numerator:

1

sec

2

θ

−

tan

2

θ

sec

2

θ

=

cos

2

θ

−

sin

2

θ

cos

2

θ

⋅

cos

2

θ

=

cos

2

θ

−

(

1

−

cos

2

θ

)

=

2

cos

2

θ

−

1

=

cos

2

θ