Question

what is the simplified form of tan (pi÷4-x)

Answer 1

tan( pi /4 -x) =(tan45-tanx)/1+tan45.tanx
                    =(1-tanx)/1+tanx

Answer 2

Answer:

Required simpliest form is $\frac{1 - tanx}{1 + tanx}$

Step-by-step explanation:

Given,

$\tan(\pi \div 4 - x)$

=$\tan( \frac{\pi}{4} - x)$

Wr want to simplify it.

We know,

$\tan(a - b) = \frac{ \tan(a) - \tan(b) }{1 + \tan(a) \tan(b) }$

Here given,

$a = \frac{\pi}{4} \: and \: b = x$

So,

$\tan( \frac{\pi}{4} - x) = \frac{ \tan( \frac{\pi}{4} ) - \tan(x) }{1 + \tan( \frac{\pi}{4} ) \tan(x) }$

Now,$\tan( \frac{\pi}{4} ) = 1$

So,

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

This is a Trigonometry problem.

Some important Trigonometry formulas,

$sin(x) = \cos(\frac{\pi}{2} - x) \\ \tan(x) = \cot(\frac{\pi}{2} - x) \\ \sec(x) = \csc(\frac{\pi}{2} - x) \\ \cos(x) = \sin(\frac{\pi}{2} - x) \\ \cot(x) = \tan(\frac{\pi}{2} - x) \\ \csc(x) = \sec(\frac{\pi}{2} - x)$

know more about Trigonometry,

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