Chapter 8 · Introduction to Trigonometry and its Applications

NCERT Exemplar Class 10 Maths Exercise 8.2

All 12 questions of NCERT Exemplar Class 10 Maths Exercise 8.2 (Introduction to Trigonometry and its Applications), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   State ​whether ​the following ​is true ​or ​false: $\frac{\tan 47^{\circ }}{\cot 43^{\circ }}=1$.
   Show answer

   True

   Step-by-step solution →
2. Q2
   The ​value of the ​expression $({\cos }^{2}23^{\circ }-{\sin }^{2}67^{\circ })$ ​is ​positive.
   Show answer

   False

   Step-by-step solution →
3. Q3
   The ​value ​of ​the expression $(\sin 80^{\circ }-\cos 80^{\circ })$ is ​negative.
   Show answer

   False

   Step-by-step solution →
4. Q4
   $\sqrt{(1-{\cos }^2\theta ){\sec }^2\theta }=\tan \theta$
   Show answer

   True

   Step-by-step solution →
5. Q5
   If $\cos A+{\cos }^{2}A=1$, ​then ${\sin }^{2}A+{\sin }^{4}A=1$.
   Show answer

   True

   Step-by-step solution →
6. Q6
   State ​whether ​the ​following is true ​or ​false ​and ​justify: $(\tan \theta +2)(2\tan \theta +1)=5\tan \theta +{\sec }^2\theta$.
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   False

   Step-by-step solution →
7. Q7
   If the length of the shadow ​of a tower ​is increasing, ​then the ​angle of elevation of ​the ​sun is also increasing.
   Show answer

   False

   Step-by-step solution →
8. Q8
   State whether the following is true or false and justify: If a man ​standing on a platform 3 metres above the surface of a lake observes ​a cloud and its reflection ​in the ​lake, then the angle ​of elevation of the cloud is ​equal to the angle of depression of its reflection.
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   False

   Step-by-step solution →
9. Q9
   State whether the following are true ​or ​false and justify: (9) The value of $2\sin \theta$ ​can be $a+\frac{1}{a}$, where $a$ is a positive number and $a\ne 1$. (10) $\cos \theta =\frac{a^2+b^2}{2ab}$, where $a$ and $b$ are ​two ​distinct ​numbers ​such ​that $ab>0$.

   1. (9)2 sin theta = a + 1/a, a > 0, a != 1
   2. (10)cos theta = (a^2 + b^2)/(2ab), a, b distinct, ab > 0
   Show answer

   Both statements are **false**. By AM-GM, $a+\frac{1}{a}>2\ge 2\sin \theta$ and $\frac{a^2+b^2}{2ab}>1\ge \cos \theta$.

   Step-by-step solution →
10. Q10
    Write ​'True' or ​'False' and justify ​your answer: $\cos \theta =\frac{a^2+b^2}{2ab}$, ​where $a$ and $b$ are ​two ​distinct numbers such that $ab>0$.
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    False

    Step-by-step solution →
11. Q11
    State whether the following statement is true or ​false and justify: The angle of elevation of ​the top of a tower is 30 degrees. If ​the ​height of ​the tower is doubled, then the angle of elevation ​of its top will also be doubled.
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    False

    Step-by-step solution →
12. Q12
    State whether the ​following is ​true or false and justify: If the height of a tower and the distance of ​the point of ​observation from its foot, both, are increased ​by 10%, then the ​angle of elevation of its top ​remains ​unchanged.
    Show answer

    True

    Step-by-step solution →