Question

tan(π\4+A) tan(π\4-A)=1 give me answer step by step​

Answer 1

Answer:

proved [ tan( π/4 + A ] * [ tan( π/4 - A ] = 1

Step-by-step explanation:

Given that

[ tan( π/4 + A ] * [ tan( π/4 - A ] = 1

To prove above equation,

Let's take

[ tan( π/4 + A ]

= [ tan( π/4 ) + tanA ] / [ 1 - tanπ/4.tanA ]

= [ 1 + tanA ] / [ 1 - tanA ] ------(1)

( since tan(π/4)= 1 )

Similarly

take [ tan( π/4 - A ]

= [ tan( π/4 ) - tanA ] / [ 1 + tanπ/4.tanA ]

= [ 1 - tanA ] / [ 1 + tanA ] ------(2)

(since tan(π/4)= 1 )

Now multiply equations(1) and (2)

we get

[ tan( π/4 + A ][ tan( π/4 - A ]

= [ 1 + tanA ][ 1 - tanA ] / [ 1 - tanA ][ 1 + tanA ]

= 1 ( Both wiil cancel itself )

Therefore,[ tan( π/4 + A ] * [ tan( π/4 - A ] = 1 is proved.

I hope it helps you. please give 5*

thank you

Answer 2

Answer:

tan(

4

π

+θ)×tan(

4

π

−θ)

1−tan

4

π

tanθ

tan

4

π

+tanθ

×

1+tan

4

π

tanθ

tan

4

π

−tanθ

1−tanθ

1+tanθ

×

1+tanθ

1−tanθ

=1

∴tan(

4

π

+θ)×tan(

4

π

−θ)=1