Class 10th Maharashtra Board Chapter 6 Trigonometry Textbook Solution.
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 6.10 | Page 131
Prove that:
`”tan A”/(1 + “tan”^2 “A”)^2 + “Cot A”/(1 + “Cot”^2 “A”)^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:
`”tanθ”/(“secθ” – 1) = (tanθ + secθ + 1)/(tanθ + secθ – 1)`
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.
ractice 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.
\[\left( \sqrt{3} = 1 . 73 \right)\]
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)