Question

the value of
$\tan( \frac{\pi}{4} + a) + \tan( \frac{\pi}{4} + a )$
​

Answer 1

Answer:

⋆

question

\tan( \frac{\pi}{4} + \theta) = \frac{ \cos\theta + \sin\theta }{ \cos\theta - \sin\theta }tan(

4

π

+θ)=

cosθ−sinθ

cosθ+sinθ

\begin{gathered}\huge \green{\underline{ solution}} \\ \\ \\using \: identities \: \implies \\ \red{ \star} \: tan \: \frac{ \pi}{4} = 1 \\ \red{ \star} \: tan \theta = \frac{sin \theta}{cos \theta} \\ \red{ \star} \: tan(x + y) = \frac{tanx + tany}{1 - tanx.tany} \\ \\ step - \: by \: step - \: explanation \\ \\ \star firstly \: taking \: left \: hand \: side \\ \implies \: tan( \frac{ \pi}{4} + \theta) \\ \\ using \: given \: identity \\ \implies \: \frac{tan \frac{ \pi}{4} + tan \theta}{1 - tan \frac{ \pi}{4}.tan \theta } \\ \\ \implies \: \frac{1 + \frac{sin \theta}{cos \theta} }{1 - \frac{sin \theta}{cos \theta} } \\ \\ \implies \red{taking \: LCM }\\ \\ \implies \frac{ \frac{cos \theta + sin \theta}{cos \theta} }{ \frac{cos \theta - sin \theta}{cos \theta} } \\ \\ \implies \: \frac{cos \theta + sin \theta}{cos \theta - sin \theta} \\ left \: hand \: side \: = right \: hand \: side \: \\ \\ hence\: proved\end{gathered}

solution

usingidentities⟹

⋆tan

4

π

=1

⋆tanθ=

cosθ

sinθ

⋆tan(x+y)=

1−tanx.tany

tanx+tany

step−bystep−explanation

⋆firstlytakinglefthandside

⟹tan(

4

π

+θ)

usinggivenidentity

⟹

1−tan

4

π

.tanθ

tan

4

π

+tanθ

⟹

1−

cosθ

sinθ

1+

cosθ

sinθ

⟹takingLCM

⟹

cosθ

cosθ−sinθ

cosθ

cosθ+sinθ

⟹

cosθ−sinθ

cosθ+sinθ

lefthandside=righthandside

henceproved

Step-by-step explanation:

Hope it helps you..

Answer 2

Answer:

answer for the given problem is given