Question

tan(pi/4+theta).tan(3pi/4+theta)

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The value   $tan(\pi /4 + \theta).tan(3\pi /4+\theta)$ is -1

Step-by-step explanation:

We have an expression $tan(\pi /4 + \theta).tan(3\pi /4+\theta)$ and we have to calculate the value of this expression by using trigonometrical properties

Step 1 of 2

For solving the above expression we have to use the following identity

$Tan (A+B)=\frac{Tan A+ Tan B}{1-TanA Tan B}$

and here when we use this property for

$tan(\pi /4 + \theta) ,andtan(3\pi /4+\theta)$ then we can write the expression as

Step 2 of 2

$tan(\pi /4 + \theta).tan(3\pi /4+\theta)=[\frac{tan\p(\pi /4) +tan\theta}{1-tan(\pi /4)tan\theta}]$*$[\frac{tan(3\pi /4)+tan \theta}{1-tan(3\pi /4)tan\theta}$

now

$tan(45)=1\\and tan(135)=-1$ then

$tan(\pi /4 + \theta).tan(3\pi /4+\theta)=\frac{1+tan\theta}{1-tan\theta}*\frac{-1+tan\theta}{1+tan\theta}$

⇒$tan(\pi /4 + \theta).tan(3\pi /4+\theta)=-1$

Hence the solution of the expression $tan(\pi /4 + \theta).tan(3\pi /4+\theta)$ is -1