10th Maths - Book Back Answers - Chapter 6 Unit - Excercise 6.5 - English Medium Guides

 

SSLC / 10th - Maths - Book Back Answers - Chapter 6 Unit Excercise 6.5 - English Medium

Tamil Nadu Board 10th Standard Maths - Chapter 6 Unit Exercise 6.5: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 6 Unit Exercise 6.5 – Maths from the Tamil Nadu State Board 10th Standard textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Chapter 6 Unit Exercise 6.5 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 10 students! Prepare well and aim for top scores. Thank you!

Chapter 6 Trigonometry Unit Ex 6.5

1. The value of is $\mathbf{s}\mathbf{i}{\mathbf{n}}^{\mathbf{2}}\mathit{\theta }\mathbf{+}\frac{\mathbf{1}}{\mathbf{1}\mathbf{+}\mathbf{t}\mathbf{a}{\mathbf{n}}^{\mathbf{2}}\mathit{\theta }}$ equal to
(A) ${\tan }^2\theta$
(B) 1
(C) ${\cot }^2\theta$
(D) 0

Answer Key:

(B) 1

 
2. tan$\mathrm{<b>\theta </b>}$$\mathbf{c}\mathbf{o}\mathbf{s}\mathit{e}{\mathit{c}}^{\mathbf{2}}\mathit{\theta }$ - tan$\mathrm{<b>\theta </b>}$ is equal to
(A) sec$\theta$
(B) ${\cot }^2\theta$
(C) sin$\theta$
(D) cot$\theta$

Answer Key:

(D) cot$\theta$

$$
3. If (sin𝛼+ cosec𝛼)² + (cos𝛼+ sec𝛼)² = k + tan²𝛼 + cot²𝛼, then the value of k is equal to
(A) 9
(B) 7
(C) 5
(D) 3

Answer Key:

(B) 7  

 

4. If sin$\mathrm{<b>\theta </b>}$ + cos$\mathrm{<b>\theta </b>}$ = a and sec$\mathrm{<b>\theta </b>}$ + cosec$\mathrm{<b>\theta </b>}$ = b , then the value of b(a² - 1) is equal to
(A) 2a
(B) 3a
(C) 0
(D) 2ab

Answer Key:

(A) 2a

 
5. If 5x = sec$\mathrm{<b>\theta \; </b>}$and 5/y = tan$\mathrm{<b>\theta </b>}$ , then ${\mathit{x}}^{\mathbf{2}}\mathbf{-}\frac{\mathbf{1}}{{\mathit{y}}^{\mathbf{2}}}$ is equal to
(A) 25
(B) 1/25
(C) 5
(D) 1

Answer Key:

(B) 1/25

 
6. If sin$\mathrm{<b>\theta </b>}$ = cos$\mathrm{<b>\theta </b>}$ , then 2 tan²$\mathrm{<b>\theta \; </b>}$+ sin²$\mathrm{<b>\theta \; </b>}$− 1 is equal to
(A) -3/2
(B) 3/2
(C) 2/3
(D) -2/3

Answer Key:

(B) 3/2

 
7. If x =a tan$\mathrm{<b>\theta </b>}$ and y =b sec$\mathrm{<b>\theta </b>}$ then
(A) $\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$
(B) $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
(C) $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

(D) $\frac{x^2}{a^2}-\frac{y^2}{b^2}=0$

Answer Key:

(A) $\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$

$\mathrm{ }$
8. (1+ tan$\mathrm{<b>\theta </b>}$ + sec$\mathrm{<b>\theta </b>}$)(1+ cot$\mathrm{<b>\theta </b>}$ − cosec$\mathrm{<b>\theta </b>}$) is equal to
(A) 0
(B) 1
(C) 2
(D) -1

Answer Key:

(C) 2

 
9. a cot$\mathrm{<b>\theta </b>}$ +b cosec$\mathrm{<b>\theta </b>}$ = p and b cot$\mathrm{<b>\theta </b>}$ +a cosec$\mathrm{<b>\theta </b>}$= q then p² - q² is equal to
(A) a² - b²
(B) b² - a²
(C) a² + b²
(D) b – a

Answer Key:

(B) b² - a²  

 
10. If the ratio of the height of a tower and the length of its shadow is 3 : 1 , then the angle of elevation of the sun has measure
(A) 45°
(B) 30°
(C) 90°
(D) 60°

Answer Key:

(D) 60°

 
11. The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to
(A) √3b
(B) b/3
(C) b/2
(D) b/√3

Answer Key:

(B) b/3

 
12. A tower is 60 m heigh. Its shadow reduces by x metres when the angle of elevation of the sun increases from 30° to 45° then x is equal to
(A) 41.92 m
(B) 43.92 m
(C) 43 m
(D) 45.6 m

Answer Key:

(B) 43.92 m 

 
13. The angle of depression of the top and bottom of 20 m tall building from the top of a multistoried building are 30° and 60° respectively. The height of the multistoried building and the distance between two buildings (in metres) is
(A) 20, 10√3
(B) 30, 5√3
(C) 20, 10
(D) 30, 10√3

Answer Key:

(D) 30, 10√3

 
14. Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is
(A) √2x
(B) x/2√2
(C) x/√2
(D) 2x

Answer Key:

(B) x/2√2

 
15. The angle of elevation of a cloud from a point h metres above a lake is β .The angle of depression of its reflection in the lake is 45°. The height of location of the cloud from the lake is
(A) $\frac{h\mathrm{(1}+tan\mathrm{\beta )}}{1-tan\beta }$
(B) $\frac{\mathrm{h(}1-tan\mathrm{\beta )}}{1+tan\beta }$
(C) h tan(45° - β)

(D) none of these 

Answer Key:

(A) $\frac{h\mathrm{(1}+tan\mathrm{\beta )}}{1-tan\beta }$