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Trigonometric Functions Maths - Trigonometric Functions

Maharashtra Board - STD 12 - Maths (MSBSHSE - Semi English Medium). 458 questions in this chapter.

Question types

Trigonometric Functions question types

458 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

458
Questions
7
Question groups
5
Question types
Sample Questions

Trigonometric Functions questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
If any ∆ABC, if a cos B = b cos A, then the triangle is ________.
  • A
    Equilateral triangle
  • ✓
    Isosceles triangle
  • C
    Scalene
  • D
    Right angled

Answer: B.

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Q 2MCQ1 Mark
If tan θ + tan 2θ + tan 3θ = tan θ∙tan 2θ∙tan 3θ, then the general value of the θ is _______.
  • A
    nπ
  • ✓
    $\frac{n \pi}{6}$
  • C
    $n \pi \pm \frac{n \pi}{4}$
  • D
    $\frac{n_\pi}{2}$

Answer: B.

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Q 3MCQ1 Mark
$\cos \left[\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{2}\right]=$
  • ✓
    $\frac{1}{\sqrt{2}}$
  • B
    $\frac{\sqrt{3}}{2}$
  • C
    $\frac{1}{2}$
  • D
    $\frac{\pi}{4}$

Answer: A.

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Q 4MCQ1 Mark
The principal value branch of $\sec ^{-1} x$ is
  • A
    $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}$
  • ✓
    $[0, \pi]-\left\{\frac{\pi}{2}\right\}$
  • C
    $(0, \pi)$
  • D
    $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.

Answer: B.

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Q 5MCQ1 Mark
$\tan \left(2 \tan ^{-1}\left(\frac{1}{5}\right)-\frac{\pi}{4}\right)=$
  • A
    $\frac{17}{7}$
  • B
    $-\frac{17}{7}$
  • C
    $\frac{7}{17}$
  • ✓
    $-\frac{7}{17}$

Answer: D.

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Q 26Do as instructed1 Mark
Find the values of the following :(i) $\sin \left[\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{3}{5}\right)\right]$
(ii) $\cos \left[\cos ^{-1}\left(-\frac{1}{2}\right)+\tan ^{-1} \sqrt{3}\right]$
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Q 27Do as instructed1 Mark
Find the values of the following(i) $\sin ^{-1}\left(\sin \frac{5 \pi}{3}\right)$
(ii) $\tan ^{-1}\left(\tan \frac{\pi}{4}\right)$
(iii) $\sin \left(\cos ^{-1}\left(-\frac{1}{\sqrt{2}}\right)\right)$
(iv) $\sin \left(\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{5}{12}\right)$
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Q 28Do as instructed1 Mark
Find the principal values of the following :
(i) $\sin ^{-1}\left(-\frac{1}{2}\right)$
(ii) $\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
(iii) $\cot ^{-1}\left(-\frac{1}{\sqrt{3}}\right)$
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Q 29Do as instructed1 Mark
In $\triangle A B C$ if $a=13, b=14, c=15$ then find the values of(i) $\cos A$
(ii) $\sin \frac{A}{2}$
(iii) $\cos \frac{A}{2}$
(iv) $\tan \frac{A}{2}$
(v) $A (\triangle ABC )$
(vi) $\sin A$
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Q 30Do as instructed1 Mark
Prove the following
(i) $2 \tan ^{-1}\left(-\frac{1}{3}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\frac{\pi}{2}$
(ii) $2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)=\frac{\pi}{4}$
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Q 32Solve the Following Question.(5 Marks)5 Marks
Show that $\frac{9 \pi}{8}-\frac{9}{4} \sin ^{-1} \frac{1}{3}=\frac{9}{4} \sin ^{-1} \frac{2 \sqrt{2}}{3}$.

Question is modified

Show that $\frac{9 \pi}{8}-\frac{9}{4} \sin ^{-1}\left(\frac{1}{3}\right)=\frac{9}{4} \sin ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)$.

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Q 34Solve the Following Question.(5 Marks)5 Marks
In $\triangle \mathrm{ABC}$ if $\mathrm{a}^2, \mathrm{~b}^2, \mathrm{c}^2$, are in A.P. then $\cot \frac{A}{2}, \cot \frac{B}{2}, \cot \frac{C}{2}$ are also in A.P.

In $\triangle \mathrm{ABC}$ if $\mathrm{a}, \mathrm{b}, \mathrm{c}_{,}$are in A.P. then $\cot \frac{A}{2}, \cot \frac{B}{2}, \cot \frac{C}{2}$ are also in A.P.

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