#### Chapters

#### Balbharati Balbharati Class 10 Mathematics 2 Geometry

## Chapter 6: Trigonometry

#### Chapter 6: Trigonometry solutions [Page 131]

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

If \[\tan \theta = \frac{3}{4}\], find the values of secθ and cosθ

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

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

If tanθ = 1 them, find the values of

Prove that:

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

Prove that:

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

Prove that:

Prove that:

Prove that:

Prove that:

Prove that:

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

Prove that:

Prove that:

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

Prove that:

Prove that:

Prove that:

#### Chapter 6: Trigonometry solutions [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.

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.

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 ?

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.

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.

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.

#### Chapter 6: Trigonometry solutions [Pages 138 - 139]

Choose the correct alternative answer for the following question.

sin\[\theta\] cosec\[\theta\]= ?

(A) 1 (B) 0 (C)\[\frac{1}{2}\] (D)\[\sqrt{2}\]

Choose the correct alternative answer for the following question.

cosec 45^{°} =?

(A)\[\frac{1}{2}\] (B) \[\sqrt{2}\] (C)\[\frac{\sqrt{3}}{2}\] (D)\[\frac{2}{\sqrt{3}}\]

Choose the correct alternative answer for the following question.

1 + tan^{2} \[\theta\] = ?

(A) cot^{2}θ (B) cosec^{2}θ (C) sec^{2}θ (D) tan^{2}θ

Choose the correct alternative answer for the following question.

(B) angle of depression.

(C) 0

(D) straight angle.

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

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

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

Prove the following.

sec*θ* (1 – sin*θ*) (sec*θ* + tan*θ*) = 1

Prove the following.

(sec*θ* + tan*θ*) (1 – sin*θ*) = cos*θ*

Prove the following.

sec^{2}*θ* + cosec^{2}*θ* = sec^{2}*θ* × cosec^{2}*θ*

Prove the following.

cot^{2}θ – tan^{2}θ = cosec^{2}θ – sec^{2}θ

Prove the following.

tan^{4}θ + tan^{2}θ = sec^{4}θ - sec^{2}θ

Prove the following.

Prove the following.

sec^{6}x – tan^{6}x = 1 + 3sec^{2}x × tan^{2}x

Prove the following.

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

Prove the following.

Prove the following.

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

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.

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.

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?

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)

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 Balbharati Class 10 Mathematics 2 Geometry

#### Textbook solutions for Class 10th Board Exam

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

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Concepts covered in Class 10th Board Exam 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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