Answers posted by thanvigandhi_1

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The value of $\cos^{-1}\bigg(\cos\frac{14\pi}{3}\bigg)$ is _____________.

answered Feb 18, 2013

Toolbox:Principal interval of cos is $([o,\pi])$$(cos(2n\pi+x)=cosx) for \;all (n\in\:N)$Ans: $( \la...

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The value of $\cos(\sin^{-1}x+\cos^{-1}x),|x|\leq 1$ is _____________.

answered Feb 18, 2013

Toolbox: $sin^{-1}x+cos^{-1}x=\large\frac{\pi}{2}$ $cos\large\frac{\pi}{2}=0$ ...

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The value of expression $\tan\bigg(\Large \frac{\sin^{-1}x+\cos^{-1}x}{2} \normalsize\bigg),when\;x=\frac{\sqrt 3}{2}$ is _______________.

answered Feb 18, 2013

Toolbox: $sin^{-1}x+cos^{-1}x=\large\frac{\pi}{2}$ for all x \( tan\large\frac{\pi...

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If $y=2\tan^{-1}x+\sin^{-1}\frac{2x}{1+x^2}$ for all x,then _________< y < ___________.

answered Feb 18, 2013

Toolbox: Put $ x=tan\theta \rightarrow \theta = tan^{-1}x$ \(\large\frac{2tan\thet...

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The result $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\bigg(\Large {\frac{x-y}{1+xy}}\normalsize \bigg)$ is true when value of xy is _____________.

answered Feb 18, 2013

$ xy > -1$

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The value of $\cot^{-1}(-x)$ for all $x\;\in\;R$ in terms of $\cot^{-1}x$ is ____________.

answered Feb 18, 2013

Toolbox: Principal interval of cot is $(0,\pi)$ $cot(\pi-\theta)=-cot\theta$ ...

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True or False: All trigonometric functions have inverse over their respective domains.

answered Feb 18, 2013

Ans - TrueBy fixing proper domain we can get inverse for all trignometric function.

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True or False: The value of the expression $(\cos^{-1}x)^2$ is equal to $\sec^2x.$

answered Feb 18, 2013

Ans - FalseBecause if $ x=cos\: A\: then \: A=cos^{-1}x$

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True or False: The domain of trigonometric functions can be restricted to any one of their branch(not necessarily principal value) in order to obtain their inverse function.

answered Feb 18, 2013

Ans - True By choosing the proper interval with the same span as that of its correspon...

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True or False: The least numerical value, either positive or negative of angle $\theta$ is called principal value of the inverse trigonometric function.

answered Feb 18, 2013

The answer is true This is the definition of principal value of inverse trignome...

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True or False:The graph of inverse trigonometric function can be obtained from the graph of their corresponding trigonometric function by interchanging x and y axes.

answered Feb 18, 2013

The answer is true Because,if (a.b) is a point on any graph of a trignometric function then...

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True or False: The minimum value of n for which $\tan^{-1}\Large {\frac{n}{\pi}}\;>\Large {\frac{\pi}{4}},\normalsize\;n\in N,$ is valid is 5

answered Feb 18, 2013

Toolbox:$\tan\large\frac{\pi}{4}=1$if $x>\large\frac{\pi}{4}$, then $\tan x >1$The value of $\...

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True or False: The principal value of $\sin^{-1}\begin{bmatrix}\cos\bigg(\sin^{-1}\frac{1}{2}\bigg)\end{bmatrix}\;is\;\Large {\frac{\pi}{3}}$

answered Feb 18, 2013

Toolbox:$\sin\large\frac{\pi}{6}=\large\frac{1}{2}$$\cos\large\frac{\pi}{6}=\large\frac{\sqrt3}{2}$$...

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