Question

Find the greatest among
$\tan^{ - 1}1 \: sin \: 1 \cos 1 \: \sin^{ - 1}1$
Pls anyone help me. I want theoretical Proof.​

Answer 1

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Class 12

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>>If [ sin^- 1 (cos^- 1 (sin...

Question

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If [sin

−1

(cos

−1

(sin

−1

(tan

−1

x)))]=1, where [ . ] denotes the greatest integer function then the values of x are

Medium

Solution

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Correct option is

A

[tansincos1,tansincossin1]

[sin

−1

(cos

−1

(sin

−1

(tan

−1

x)))]=1

then

1≤sin

−1

(cos

−1

(sin

−1

(tan

−1

x)))≤

2

Π

sin1≤cos

−1

(sin

−1

(tan

−1

x))≤1

cossin1≤sin

−1

(tan

−1

x)≤cos1

sincossin1≤tan

−1

x≤sincos1

tansincossin1≤x≤tansincos1

buttansincossin≥tansincos1

sox∈[tansincos1,tansincossin1]