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The value of sin(tan(tan^{-1}\frac{3\pi}{4})) is

Option: 1

-\frac{1}{\sqrt{2}}


Option: 2

\frac{1}{\sqrt{2}}


Option: 3

-\frac{\sqrt{3}}{2}


Option: 4

1


Answers (1)

We have learnt that

Function f (f-1 ( x )), where f(x) is a trigonometric function

\begin{array} {l}\mathrm{1.\;\;\sin(\sin^{-1}(x))=x} \quad\quad\quad \;\mathrm{for\;all\;x\in[-1,1] }\\\mathrm{2.\;\;\cos(\cos^{-1}(x))=x} \quad\quad\quad \mathrm{for\;all\;x\in[-1,1]}\\\mathrm{3.\;\;\tan(\tan^{-1}(x))=x} \;\;\;\quad\quad \mathrm{for\;all\;x\in\mathbb{R}}\\\mathrm{4.\;\;\cot(\cot^{-1}(x))=x} \quad\quad\quad \mathrm{for\;all\;x\in\mathbb{R}} \\\mathrm{5.\;\;\sec(\sec^{-1}(x))=x} \quad\quad\quad \mathrm{for\;all\;x\in\mathbb{R}-(-1,1)}\\\mathrm{6.\;\;\csc(\csc^{-1}(x))=x} \quad\quad\quad \mathrm{for\;all\;x\in\mathbb{R}-(-1,1)}\end{array}

Now,

As tan(tan^{-1}\frac{3\pi}{4})= \frac{3\pi}{4}

So,

\\sin(tan(tan^{-1}\frac{3\pi}{4}))=sin(\frac{3\pi}{4})\\=\frac{1}{\sqrt{2}}

Posted by

Kshitij

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