Assignment Details

Introduction to Trigonometry and Its Application

Note it

1500 minutes

Jan 31, 10:00 AM

80.0 marks

MCQ

40 questions

SURYA KANT SHARMA

...

Class Details

Maths

Class10th

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Question Text

Question 1 :
If $\tan 2A = \cot \begin{pmatrix}A – 18^{\circ}\end{pmatrix}$, where 2A is an acute angle, find the value of A.

Question 2 :
If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.

Question 3 :
The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is $60^\circ$ and the angle of elevation of the top of the second tower from the foot of the first tower is $30^\circ$. Find the distance between the two towers and also the height of the other tower.

Question 4 :
$sin (45^\circ + \theta) – cos (45^\circ – \theta) $ is equal to

Question 5 :
$\sin \theta = \frac{4}{3}$ for some angle $\theta$. True or False?

Question 6 :
If $\sec 4A = cosec\ \begin{pmatrix}A – 20^{\circ}\end{pmatrix}$, where 4A is an acute angle, find the value of A.

Question 7 :
In $\Delta PQR$, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of $\sin P, \cos P, \tan P$ respectively.

Question 12 :
Is $\frac{cos A – sin A + 1}{cos A + sin A - 1}= cosecA + cotA$?

Question 14 :
If one trigonometric ratio of an angle is given, the other trigonometric ratios of the angle can be determined.

Question 16 :
(sec A + tan A) (1 – sin A) = ______

Question 20 :
In triangle ABC, right-angled at B, if $\tan A = \frac{1}{\sqrt3}$, then find the value of $\cos A \cos C -\sin A\sin C$

Question 22 :
If $\tan \begin{pmatrix}A + B\end{pmatrix} = \sqrt3$, $\tan \begin{pmatrix}A - B\end{pmatrix} =\frac{1}{\sqrt3}$, $0^{\circ}< A + B ≤ 90^{\circ}$, $A > B$, find A and B respectively.

Question 25 :
If A, B and C are interior angles of a triangle ABC, then $\sin\begin{pmatrix}\frac{B+C}{2}\end{pmatrix}\ne\cos\begin{pmatrix}\frac{A}{2}\end{pmatrix}$. TRUE or FALSE ?

Question 26 :
State true or false: The value of $\tan A$ is always less than 1.

Question 27 :
Can all the other trigonometric ratios of ∠ A be written in terms of sec A?

Question 28 :
The value of $\sin \theta$ increases as $\theta$ increases. True or False?

Question 29 :
The value of $\tan A$ is always less than 1. True or False?

Question 30 :
The value of the expression $[cosec(75^\circ+ \theta) – sec (15^\circ–\theta)–tan(55^\circ + \theta) + cot(35^\circ – \theta)]$ is

Question 32 :
If $\alpha + \beta = 90^\circ$, then find the value of $\sqrt{\cos\alpha\ \operatorname{cosec}\beta-\cos\alpha\ \sin\beta}$.

Question 38 :
In triangle ABC, right-angled at B, if $\tan A = \frac{1}{\sqrt3}$, then find the value of $\sin A \cos C +\cos A\sin C$

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