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Balbharati solutions for Class 10th Board Exam Geometry chapter 6 - Trigonometry

Textbook for SSC Class 10 Mathematics 2

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Chapters

Balbharati SSC Class 10 Mathematics 2

Textbook for SSC Class 10 Mathematics 2

Chapter 6: Trigonometry

Chapter 6: Trigonometry solutions [Page 131]

Q 1 | Page 131

If \[\sin\theta = \frac{7}{25}\], find the values of cosθ and tan​θ.

Q 2 | Page 131

If \[\tan \theta = \frac{3}{4}\], find the values of sec​θ and cos​θ

Q 3 | Page 131

If \[\cot\theta = \frac{40}{9}\], find the values of cosecθ and sinθ.

Q 4 | Page 131

If 5 secθ – 12 cosecθ = 0, find the values of secθ, cosθ and sinθ.

Q 5 | Page 131

If tanθ = 1 them, find the values of

\[\frac{\sin\theta + \cos\theta}{\sec\theta + cosec\theta}\]
Q 6.01 | Page 131

Prave that:
\[\frac{\sin^2 \theta}{\cos\theta} + \cos\theta = \sec\theta\]

Q 6.02 | Page 131

Prave that:

\[\cos^2 \theta\left( 1 + \tan^2 \theta \right) = 1\]

Q 6.03 | Page 131

Prave that:

\[\sqrt{\frac{1 - \sin\theta}{1 + \sin\theta}} = \sec\theta - \tan\theta\]

 

Q 6.04 | Page 131

Prave that:

\[\left( \sec\theta - \cos\theta \right)\left( \cot\theta + \tan\theta \right) = \tan\theta \sec\theta\]
Q 6.05 | Page 131

Prave that:

\[\cot\theta + \tan\theta = cosec\theta \sec\theta\]
Q 6.06 | Page 131

Prave that:

\[\frac{1}{\sec\theta - \tan\theta} = \sec\theta + \tan\theta\]
Q 6.07 | Page 131

Prave that:
\[\sec^4 \theta - \cos^4 \theta = 1 - 2 \cos^2 \theta\]

Q 6.08 | Page 131

Prave that:

\[\sec\theta + \tan\theta = \frac{\cos\theta}{1 - \sin\theta}\]
Q 6.09 | Page 131

Prave that:
If \[\tan\theta + \frac{1}{\tan\theta} = 2\], then show that \[\tan^2 \theta + \frac{1}{\tan^2 \theta} = 2\]

Q 6.1 | Page 131

Prove that:

\[\frac{\tan A}{\left( 1 + \tan^2 A \right)^2} + \frac{\cot A}{\left( 1 + \cot^2 A \right)^2} = \sin A \cos A\]
Q 6.11 | Page 131

Prove that:

\[\sec^4 A\left( 1 - \sin^4 A \right) - 2 \tan^2 A = 1\]
Q 6.12 | Page 131

Prove that:

\[\frac{\tan\theta}{\sec\theta - 1} = \frac{\tan\theta + \sec\theta + 1}{\tan\theta + \sec\theta - 1}\]

Chapter 6: Trigonometry solutions [Page 137]

Q 1 | Page 137

A person is standing at a distance of 80 m from a church looking at its top. The angle of elevation is of 45°. Find the height of the church.

Q 2 | Page 137

From the top of a lighthouse, an observer looking at a ship makes angle of depression of 60°. If the height of the lighthouse is 90 metre, then find how far the ship is from the lighthouse.

\[\left( \sqrt{3} = 1 . 73 \right)\]
Q 3 | Page 137

Two buildings are facing each other on a road of width 12 metre. From the top of the first building, which is 10 metre high, the angle of elevation of the top of the second is found to be 60°. What is the height of the second building ?

Q 4 | Page 137

Two poles of heights 18 metre and 7 metre are erected on a ground. The length of the wire fastened at their tops in 22 metre. Find the angle made by the wire with the horizontal.

Q 5 | Page 137

A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60° with the horizontal. Find the height of the tree.

Q 6 | Page 137

A kite is flying at a height of 60 m above the ground. The string attached to the kite is tied at the ground. It makes an angle of 60° with the ground. Assuming that the string is straight, find the length of the string.

\[\left( \sqrt{3} = 1 . 73 \right)\]

Chapter 6: Trigonometry solutions [Pages 138 - 139]

Q 1.1 | Page 138

Choose the correct alternative answer for the following question.
sin\[\theta\] cosec\[\theta\]= ?
(A) 1  (B) 0  (C)\[\frac{1}{2}\]   (D)\[\sqrt{2}\]

Q 1.2 | Page 138

Choose the correct alternative answer for the following question.
cosec 45° =?
(A)\[\frac{1}{2}\]  (B) \[\sqrt{2}\]  (C)\[\frac{\sqrt{3}}{2}\]  (D)\[\frac{2}{\sqrt{3}}\]

Q 1.3 | Page 138

Choose the correct alternative answer for the following question.

1 + tan2 \[\theta\]  = ?

(A) cot2θ  (B) cosec2θ  (C) sec2θ   (D) tan2θ

Q 1.4 | Page 138

Choose the correct alternative answer for the following question.

When we see at a higher level , from the horizontal line,angle formed is ....... .
(A) angle of elevation.
(B) angle of depression.
(C) 0
(D) straight angle.
Q 2 | Page 138

If \[\sin\theta = \frac{11}{61}\], find the values of cosθ using trigonometric identity.

Q 3 | Page 138

If tanθ = 2, find the values of other trigonometric ratios.

 
Q 4 | Page 138

If \[\sec\theta = \frac{13}{12}\], find the values of other trigonometric ratios.

Q 5.01 | Page 138

Prove the following.
secθ (1 – sinθ) (secθ + tanθ) = 1

Q 5.02 | Page 138

Prove the following.
(secθ + tanθ) (1 – sinθ) = cosθ

Q 5.03 | Page 138

Prove the following.
sec2θ + cosec2θ = sec2θ × cosec2θ

Q 5.04 | Page 138

Prove the following.
cot2θ – tan2θ = cosec2θ – sec2θ

Q 5.05 | Page 138

Prove the following.

\[\frac{1}{1 - \sin\theta} + \frac{1}{1 + \sin\theta} = 2 \sec^2 \theta\]
Q 5.06 | Page 138

Prove the following.

\[\frac{1}{1 - \sin\theta} + \frac{1}{1 + \sin\theta} = 2 \sec^2 \theta\]
Q 5.07 | Page 138

Prove the following.
sec6x – tan6x = 1 + 3sec2x × tan2x

Q 5.08 | Page 138

Prove the following.
\[\frac{\tan\theta}{sec\theta + 1} = \frac{sec\theta - 1}{\tan\theta}\]

Q 5.09 | Page 138

Prove the following.

\[\frac{\tan^3 \theta - 1}{\tan\theta - 1} = \sec^2 \theta + \tan\theta\]
Q 5.1 | Page 138

Prove the following.
\[\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac{1}{\sin\theta - \tan\theta}\]

Q 6 | Page 139

A boy standing at a distance of 48 meters from a building observes the top of the building and makes an angle of elevation of 30°. Find the height of the building.

 
Q 7 | Page 139

From the top of the light house, an observer looks at a ship and finds the angle of depression to be 30°. If the height of the light-house is 100 meters, then find how far the ship is from the light-house.

Q 8 | Page 139

Two buildings are in front of each other on a road of width 15 meters. From the top of the first building, having a height of 12 meter, the angle of elevation of the top of the second building is 30°.What is the height of the second building?

Q 9 | Page 139

A ladder on the platform of a fire brigade van can be elevated at an angle of 70° to the maximum. The length of the ladder can be extended upto 20 m. If the platform is 2m above the ground, find the maximum height from the ground upto which the ladder can reach. (sin 70° = 0.94)

Q 10 | Page 139

While landing at an airport, a pilot made an angle of depression of 20°. Average speed of the plane was 200 km/hr. The plane reached the ground after 54 seconds. Find the height at which the plane was when it started landing. (sin 20° = 0.342)

Chapter 6: Trigonometry

Balbharati SSC Class 10 Mathematics 2

Textbook for SSC Class 10 Mathematics 2

Balbharati solutions for Class 10th Board Exam Geometry chapter 6 - Trigonometry

Balbharati solutions for Class 10th Board Exam Geometry chapter 6 (Trigonometry) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Textbook for SSC Class 10 Mathematics 2 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10th Board Exam Geometry chapter 6 Trigonometry are Application of Trigonometry, Heights and Distances, Trigonometric Ratios of Complementary Angles, Trigonometric Identities, Trigonometric Ratios in Terms of Coordinates of Point, Angles in Standard Position, Trigonometry Ratio of Zero Degree and Negative Angles.

Using Balbharati Class 10th Board Exam solutions Trigonometry exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board Class 10th Board Exam prefer Balbharati Textbook Solutions to score more in exam.

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