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Engineering
94 Views   |

If $tan \left ( cos^{-1}x \right )= Sin\left ( cot^{-1}\frac{1}{2} \right )$   then x is equal to

• Option 1)

$\pm \frac{5}{3}$

• Option 2)

$\pm \frac{\sqrt{5}}{3}$

• Option 3)

$\pm \frac{5}{\sqrt{3}}$

• Option 4)

None of these

As we learnt in  Relation between all the Inverse Trigonometric Functions - - wherein This happens with domain of functions, x0       Option 1) Incorrect Option 2) Correct Option 3) Incorrect Option 4) None of these Incorrect
Engineering
100 Views   |

If $Sin ^{-1}x=\frac{\pi}{5}$   for some   $x\epsilon \left ( -1,1 \right )$   then value of  $cos^{-1}x\, \, is$

• Option 1)

$\frac{3\pi}{10}$

• Option 2)

$\frac{5\pi}{10}$

• Option 3)

$\frac{7\pi}{10}$

• Option 4)

$\frac{9\pi}{10}$

As we learnt in  Important Results of Inverse Trigonometric Functions - - wherein When      Option 1) Correct Option 2) Incorrect Option 3) Incorrect Option 4) Incorrect
Engineering
151 Views   |

A ladder 40m long rests against a wall. If the feet of the ladder is 20m from the wall, then the angle of elevation is

• Option 1)

$30^{\circ}$

• Option 2)

$45^{\circ}$

• Option 3)

$60^{\circ}$

• Option 4)

$90^{\circ}$

As we discussed in concept Trigonometric Ratios of Functions - - wherein     Option 1) This option is incorrect. Option 2) This option is incorrect. Option 3) This option is correct. Option 4) This option is incorrect.
Engineering
155 Views   |

A circus artist is climbing from the ground along a rope, stretched from the top of vertical pole and tied at the ground. The height of the pole is 8m and the angle made by the rope with the ground level is $30^{\circ}$. The distance covered by the artist in climbing to the top of the hole is

• Option 1)

$\frac{24\sqrt{3}}{3}$m

• Option 2)

$\frac{16\sqrt{3}}{3}$m

• Option 3)

24m

• Option 4)

16m

As we discussed in concept Trigonometric Ratios of Functions - - wherein     OA = 16 Option 1) m This option is incorrect. Option 2) m This option is incorrect. Option 3) 24m This option is incorrect. Option 4) 16m This option is correct.
Engineering
212 Views   |

A beach rescue helicopter at an altitude of 250m from the surface of the sea finds two persons sinking in the sea. If the angle of depression for the persons in the opposite directions are $60^{\circ}$ and $30^{\circ}$, find the distance between the two persons.

• Option 1)

$\frac{100}{\sqrt{3}-1}$ m

• Option 2)

$\frac{1000}{\sqrt{3}+1}$ m

• Option 3)

$\frac{1000\sqrt{3}}{3}$ m

• Option 4)

$\frac{1000}{\sqrt{3}}$ m

As learnt in Trigonometric Ratios of Functions - - wherein    From figure and   Option 1)  m This option is incorrect Option 2) m This option is incorrect Option 3) m This option is incorrect Option 4) m This option is correct
Engineering
103 Views   |

$Sec^{2}\left ( tan^{-1}2 \right )+ cosec^{2}\left ( cot^{-1}3 \right )$  is equal to

• Option 1)

5

• Option 2)

13

• Option 3)

15

• Option 4)

6

Option 1) 5 This option is incorrect Option 2) 13 This option is incorrect Option 3) 15 This option is correct Option 4) 6 This option is incorrect
Engineering
92 Views   |

$2\sin ^{2}B+ 4\cos (A+B) \sin A \sin B+ \cos 2 (A+B)$

• Option 1)

$\sin 2A$

• Option 2)

$\cos 2B$

• Option 3)

$\cos 2A$

• Option 4)

$\sin 2B$

As we learnt in  Double Angle Formula - - wherein These are formulae for double angles.     Option 1) This option is incorrect Option 2) This option is incorrect Option 3) This option is correct Option 4) This option is incorrect
Engineering
407 Views   |

$\tan 3A-\tan 2A-\tan A$ is equal to

• Option 1)

$-tan 3A \tan 2A \tan A$

• Option 2)

$\tan A \tan 2A \tan 3A$

• Option 3)

$\tan A \tan 2A - \tan 2A \tan 3A - \tan 3A \tan A$

• Option 4)

None of these

As learnt in Triple Angle Formula - - wherein These are formulae for triple angles.     Double Angle Formula - - wherein These are formulae for double angles.                           Option 1) This option is incorrect Option 2) This option is correct Option 3) This option is incorrect Option 4) None of these This option is incorrect
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