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1: Real Numbers
Algebra
2: Polynomials
3: Linear Equations in Two Variables
4: Quadratic Equations
5: Arithmetic Progression
Coordinate Geometry
6: Coordinate Geometry
Geometry
7: Triangles
8: Circles
9: Constructions
Trigonometry
10: Trignometric Ratios
▶ 11: T-Ratios of Some Particular Angles
12: Trigonometric Ratios of Some Complemantary Angles
13: Trigonometric identities
14: Heights and Distances
Mensuration
15: Perimeter And Area of Plane Figures
16: Area of Circle, Sector and Segment
17: Volumes and Surface Areas of Solids
Statistics and Probability
18: Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive
19: Probability
Chapter 20: Additional Questions
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Solutions for Chapter 11: T-Ratios of Some Particular Angles
Below listed, you can find solutions for Chapter 11 of CBSE, Karnataka Board R.S. Aggarwal for Mathematics [English] Class 10.
R.S. Aggarwal solutions for Mathematics [English] Class 10 11 T-Ratios of Some Particular Angles EXERCISE 11 [Pages 572 - 574]
Evaluate the following:
sin 60° cos 30° + cos 60° sin 30°
Evaluate the following:
sin 60° cos 30° – cos 60° sin 30°
Evaluate the following:
cos 60° cos 30° – sin 60° sin 30°
Evaluate the following:
cos 45° cos 30° + sin 45° sin 30°
Evaluate the following:
tan 30° cosec 60° + tan 60° sec 30°
Evaluate the following:
2cos260° + 3sin245° – 3sin230° + 2cos290°
Evaluate the following:
`sin^2 30^circ cos^2 45^circ + 4tan^2 30^circ + 1/2 sin^2 90^circ + 1/8 cot^2 60^circ`
Evaluate the following:
`cot^2 30^circ - 2cos^2 30^circ - 3/4 sec^2 45^circ + 1/4 "cosec"^2 30^circ`
Evaluate the following:
(cos 0° + sin 45° + sin 30°)(sin 90° – cos 45° + cos 60°)
Show that `(1 - sin 60^circ)/(cos 60^circ) = (tan 60^circ - 1)/(tan 60^circ + 1)`.
Show that `(cos 30^circ + sin 60^circ)/(1 + sin 30^circ + cos 60^circ) = cos 30^circ`.
Verify the following:
sin 60° cos 30° – cos 60° sin 30° = sin 30°
Verify the following:
cos 60° cos 30° + sin 60° sin 30° = cos 30°
Verify the following:
2 sin 30° cos 30° = sin 60°
Verify the following:
2 sin 45° cos 45° = sin 90°
If A = 45°, verify that sin 2A = 2 sin A cos A.
If A = 45°, verify that cos 2A = 2 cos2A – 1 = 1 – 2 sin2A.
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2A)`.
If A = 30°, verify that `cos 2A = (1 - tan^2A)/(1 + tan^2A)`.
If A = 30°, verify that `tan 2A = (2 tan A)/(1 - tan^2A)`.
If A = 60° and B = 30°, verify that sin (A + B) = sin A cos B + cos A sin B.
If A = 60° and B = 30°, verify that cos (A + B) = cos A cos B – sin A sin B.
If A = 60° and B = 30°, verify that sin (A – B) = sin A cos B – cos A sin B.
If A = 60° and B = 30°, verify that cos (A – B) = cos A cos B + sin A sin B.
If A = 60° and B = 30°, verify that `tan (A - B) = (tan A - tan B)/(1 + tan A tan B)`.
If A and B are acute angles such that `tan A = 1/3, tan B = 1/2` and `tan (A + B) = (tan A + tan B)/(1 - tan A tan B)`, show that A + B = 45°.
Using the formula, `tan 2A = (2 tan A )/(1 - tan^2 A)`, find the value of tan 60°, it being given that `tan 30^circ = 1/sqrt(3)`.
Using the formula, `cos A = sqrt((1 + cos2A)/2)`, find the value of cos 30°, it being given that `cos 60^circ = 1/2`.
Using the formula, `sin A = sqrt((1 - cos 2A)/2)`, find the value of sin 30°, it being given that `cos 60^circ = 1/2`.
If sin (A + B) = sin A cos B + cos A sin B and cos (A – B) = cos A cos B + sin A sin B, find the values of (i) sin 75° (ii) cos 15°.
HINT: Take A = 45° and B = 30°.
If tan (x + 30°) = 1 then find the value of x.
If `(cot θ - 1)/(cot θ + 1) = (1 - sqrt(3))/(1 + sqrt(3))` then find the acute angle θ.
If sin (A + B) = 1 and `tan (A - B) = 1/sqrt(3)`, 0° < (A + B) ≤ 90° and A > B then find the values of A and B.
If `sin (A + B) = sqrt(3)/2` and `cos (A - B) = sqrt(3)/2`, 0° < (A + B) ≤ 90° and A > B then find the values of A and B.
If `tan (A - B) = 1/sqrt(3)` and `tan (A + B) = sqrt(3)`, 0° < (A + B) ≤ 90° and A > B then find the values of A and B.
If cosec (A + B) = 1 and cosec (A – B) = 2, 0° < (A + B) ≤ 90° and A > B then find the values of:
(i) sin A cos B + cos A sin B
(ii) `(tan A - tan B)/(1 + tan A tan B)`
If 3x = cosec θ and `3/x = cot θ`, find the value of `3(x^2 - 1/x^2)`.
In the adjoining figure, ΔABC is a right-angled triangle in which ∠B = 90°, ∠A = 30° and AC = 20 cm. Find (i) BC, (ii) AB.
In the adjoining figure, ΔABC is right-angled at B and ∠A = 30°. If BC = 6 cm, find (i) AB, (ii) AC.
In the adjoining figure, ΔABC is right-angled at B and ∠A = 45°. If AC = `3sqrt(2)` cm, find (i) BC, (ii) AB.
Find the value of x for which x tan 45° cot 60° = sin 30° cosec 60°.
Find the value of x for which `2 "cosec"^2 30^circ + x sin^2 60^circ - 3/4 tan^2 30^circ = 10`.
R.S. Aggarwal solutions for Mathematics [English] Class 10 11 T-Ratios of Some Particular Angles MULTIPLE-CHOICE QUESTIONS (MCQ) [Pages 576 - 577]
Choose the correct answer in each of the following questions:
(sec260° – 1) = ?
0
2
3
4
(sin230° – sec260° + 4cot245°) = ?
4
2
1
`1/4`
(3 cos260° + 2 cot230° – 5 sin245°) = ?
1
4
`17/4`
`13/6`
`(cos^2 30^circ cos^2 45^circ + 4 sec^2 60^circ + 1/2 cos^2 90^circ - 2 tan^2 60^circ)` = ?
`81/8`
`83/8`
`73/8`
`75/8`
(cos 0° + sin 30° + sin 45°)(sin 90° + cos 60° – cos 45°) = ?
`7/4`
`5/6`
`3/5`
`5/8`
If tan245° – cos230° = x sin 45° cos 45° then x = ?
2
–2
`1/2`
`-1/2`
If `sqrt(2) sin (60^circ - α) = 1` then α = ?
15°
30°
45°
60°
If tan x = 3 cot x then x = ?
60°
45°
30°
15°
If `sqrt(3) tan 2θ - 3 = 0` then θ = ?
15°
30°
45°
60°
If `2 sin 2θ = sqrt(3)` then θ = ?
30°
45°
60°
90°
If 2 cos 3θ = 1 then θ = ?
10°
15°
20°
30°
If x tan 45° cos 60° = sin 60° cot 60° then x = ?
1
`1/2`
`1/sqrt(2)`
`sqrt(3)`
If tan (3x + 30°) = 1 then x = ?
20°
15°
10°
5°
If sin θ = cos θ, 0 ≤ θ ≤ 90° then θ = ?
30°
45°
60°
90°
If `sin (A - B) = 1/2` and `cos (A + B) = 1/2`, 0° < (A + B) ≤ 90° and A > B then values of A and B are ______.
(60°, 30°)
(60°, 15°)
(45°, 15°)
(60°, 25°)
Solutions for 11: T-Ratios of Some Particular Angles
R.S. Aggarwal solutions for Mathematics [English] Class 10 chapter 11 - T-Ratios of Some Particular Angles
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