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Balbharati solutions for Maharashtra state board (SSC) 10th Standard Maths 2 Geometry chapter 6 - Trigonometry [Latest edition]

Chapters

Chapter 6: Trigonometry

Practice Set 6.1Practice Set 6.2Problem Set 6
Practice Set 6.1 [Page 131]

Balbharati solutions for Maharashtra state board (SSC) 10th Standard Maths 2 Geometry Chapter 6 Trigonometry Practice Set 6.1 [Page 131]

Practice Set 6.1 | Q 1 | Page 131

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

Practice Set 6.1 | Q 2 | Page 131

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

Practice Set 6.1 | Q 3 | Page 131

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

Practice Set 6.1 | Q 4 | Page 131

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

Practice Set 6.1 | Q 5 | Page 131

If tanθ = 1 them, find the values of

\[\frac{\sin\theta + \cos\theta}{\sec\theta + cosec\theta}\]
Practice Set 6.1 | Q 6.01 | Page 131

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

Practice Set 6.1 | Q 6.02 | Page 131

Prove that:

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

Practice Set 6.1 | Q 6.03 | Page 131

Prove that:

\[\sqrt{\frac{1 - \sin\theta}{1 + \sin\theta}} = \sec\theta - \tan\theta\]
Practice Set 6.1 | Q 6.04 | Page 131

Prove that:

\[\left( \sec\theta - \cos\theta \right)\left( \cot\theta + \tan\theta \right) = \tan\theta \sec\theta\]
Practice Set 6.1 | Q 6.05 | Page 131

Prove that:

\[\cot\theta + \tan\theta = cosec\theta \sec\theta\]
Practice Set 6.1 | Q 6.06 | Page 131

Prove that:

\[\frac{1}{\sec\theta - \tan\theta} = \sec\theta + \tan\theta\]
Practice Set 6.1 | Q 6.07 | Page 131

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

Practice Set 6.1 | Q 6.08 | Page 131

Prove that:

\[\sec\theta + \tan\theta = \frac{\cos\theta}{1 - \sin\theta}\]
Practice Set 6.1 | Q 6.09 | Page 131

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

Practice Set 6.1 | Q 6.1 | Page 131

Prove that:

\[\frac{\tan A}{\left( 1 + \tan^2 A \right)^2} + \frac{\cot A}{\left( 1 + \cot^2 A \right)^2} = \sin A \cos A\]
Practice Set 6.1 | Q 6.11 | Page 131

Prove that:

\[\sec^4 A\left( 1 - \sin^4 A \right) - 2 \tan^2 A = 1\]
Practice Set 6.1 | Q 6.12 | Page 131

Prove that:

\[\frac{\tan\theta}{\sec\theta - 1} = \frac{\tan\theta + \sec\theta + 1}{\tan\theta + \sec\theta - 1}\]
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Practice Set 6.2 [Page 137]

Balbharati solutions for Maharashtra state board (SSC) 10th Standard Maths 2 Geometry Chapter 6 Trigonometry Practice Set 6.2 [Page 137]

Practice Set 6.2 | 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.

Practice Set 6.2 | 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.

\[\left( \sqrt{3} = 1 . 73 \right)\]
Practice Set 6.2 | 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 ?

Practice Set 6.2 | 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.

Practice Set 6.2 | 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.

Practice Set 6.2 | 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.

\[\left( \sqrt{3} = 1 . 73 \right)\]
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Problem Set 6 [Pages 138 - 139]

Balbharati solutions for Maharashtra state board (SSC) 10th Standard Maths 2 Geometry Chapter 6 Trigonometry Problem Set 6 [Pages 138 - 139]

Problem Set 6 | Q 1.1 | Page 138

Choose the correct alternative answer for the following question.
sin \[\theta\] cosec \[\theta\]= ?

  • 1

  • 0

  • \[\frac{1}{2}\] 

  • \[\sqrt{2}\] 

Problem Set 6 | Q 1.2 | Page 138

Choose the correct alternative answer for the following question.
cosec 45° =?

  • \[\frac{1}{2}\]

  • \[\sqrt{2}\] 

  • \[\frac{\sqrt{3}}{2}\] 

  • \[\frac{2}{\sqrt{3}}\] 

Problem Set 6 | Q 1.3 | Page 138

Choose the correct alternative answer for the following question.

1 + tan2 \[\theta\]  = ?

  • cot2θ 

  • cosec2θ 

  • sec2θ    

  • tan2θ

Problem Set 6 | 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 ........
 
  • angle of elevation.

  • angle of depression.

  • 0

  • straight angle.

Problem Set 6 | Q 2 | Page 138

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

Problem Set 6 | Q 3 | Page 138

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

 
Problem Set 6 | Q 4 | Page 138

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

Problem Set 6 | Q 5.01 | Page 138

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

Problem Set 6 | Q 5.02 | Page 138

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

Problem Set 6 | Q 5.03 | Page 138

Prove the following.
sec2θ + cosec2θ = sec2θ × cosec2θ 

Problem Set 6 | Q 5.04 | Page 138

Prove the following.
cot2θ – tan2θ = cosec2θ – sec2θ

Problem Set 6 | Q 5.05 | Page 138

Prove the following.

tan4θ + tan2θ = sec4θ - sec2θ

Problem Set 6 | Q 5.06 | Page 138

Prove the following.

\[\frac{1}{1 - \sin\theta} + \frac{1}{1 + \sin\theta} = 2 \sec^2 \theta\]
Problem Set 6 | Q 5.07 | Page 138

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

Problem Set 6 | Q 5.08 | Page 138

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

Problem Set 6 | Q 5.09 | Page 138

Prove the following.

\[\frac{\tan^3 \theta - 1}{\tan\theta - 1} = \sec^2 \theta + \tan\theta\]
Problem Set 6 | Q 5.1 | Page 138

Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`

Problem Set 6 | 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.

 
Problem Set 6 | 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.

Problem Set 6 | 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?

Problem Set 6 | 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)

Problem Set 6 | 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)

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Chapter 6: Trigonometry

Practice Set 6.1Practice Set 6.2Problem Set 6

Balbharati solutions for Maharashtra state board (SSC) 10th Standard Maths 2 Geometry chapter 6 - Trigonometry

Balbharati solutions for Maharashtra state board (SSC) 10th Standard Maths 2 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 Maharashtra state board (SSC) 10th Standard Maths 2 Geometry solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Maharashtra state board (SSC) 10th Standard Maths 2 Geometry chapter 6 Trigonometry are Trigonometry Ratio of Zero Degree and Negative Angles, 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.

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