Math, asked by gurijatt3243, 10 months ago

Tan(π/4+A)×tan(3π/4+A)=-1

Answers

Answered by songsar22
0

Answer:

oh no

Step-by-step explanation:

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Answered by Anonymous
1

 \tan = ( \frac{ \pi}{4}  + a)  \times  \tan( \frac{3 \pi + A}{4} )

using \: tangent \: sum \: of \: angle \: formula \ratio -

 tan(A+B) =  \frac{ \tan A+ \tan B}{1 -  \tan A \times  \tan B }

 in \: conjuction \: with \ratio

\tan( \frac{ \tan \pi }{4} )  = 1 \: and \: \tan( \frac{ \tan 3\pi }{4} ) =  - 1

now

\tan(  \frac{\pi}{4}   + A) \times  \tan( \frac{3 \pi }{4}  + A)

=  \frac{ \tan (\frac{ \pi }{4} ) +  \tan  A}{1 -  \tan( \frac{ \pi }{4}) \times  \tan A  }

=  > \frac{ \tan (\frac{3 \pi }{4} ) +  \tan  A}{1 -  \tan( \frac{ 3\pi }{4}) \times  \tan A  }

=   \frac{1 +  \tan A }{1 -  \tan A}  \times  \frac{ - 1 +  \tan A }{1 +  \tan A}

= \frac{ - 1 +  \tan A }{1  -   \tan A} \times \frac{  1  -   \tan A }{1 +  \tan A}

\boxed{=  - 1}

HENCE, R.H.S = L.H.S

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