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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
![R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० chapter 12 - Trigonometric Ratios of Some Complemantary Angles - Shaalaa.com](/images/mathematics-english-class-10_6:8f062ea57bdf49abb4f6d22550b39d56.jpg "R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० chapter 12 - Trigonometric Ratios of Some Complemantary Angles")
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Solutions for Chapter 12: Trigonometric Ratios of Some Complemantary Angles
Below listed, you can find solutions for Chapter 12 of CBSE, Karnataka Board R.S. Aggarwal for मैथमैटिक्स [अंग्रेजी] कक्षा १०.
R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० 12 Trigonometric Ratios of Some Complemantary Angles EXERCISE 12 [Pages 590 - 591]
Without using trigonometric tables, evaluate:
`(sin 26^circ)/(cos 64^circ)`
Without using trigonometric tables, evaluate:
`sec 11^circ/("cosec" 79^circ)`
Without using trigonometric tables, evaluate:
`(tan 65^circ)/(cot 25^circ)`
Without using trigonometric tables, evaluate:
`(cos 37^circ)/(sin 53^circ)`
Without using trigonometric tables, evaluate:
`("cosec" 42^circ)/sec 48^circ`
Without using trigonometric tables, evaluate:
`(tan 35^circ)/(cot 55^circ) + (cot 78^circ)/(tan 12^circ) = 2`
Without using trigonometric tables, prove that:
cos 81° – sin 9° = 0
Without using trigonometric tables, prove that:
tan 71° – cot 19° = 0
Without using trigonometric tables, prove that:
cosec 60° – sec 30° = 0
Without using trigonometric tables, prove that:
cot 34° – tan 56° = 0
Without using trigonometric tables, prove that:
sin248° + sin242° = 1
Without using trigonometric tables, prove that:
cos272° + cos218° = 1
Without using trigonometric tables, prove that:
sin212° + sin278° = 1
Without using trigonometric tables, prove that:
sec229° – cot261° = 1
Without using trigonometric tables, prove that:
tan256° – cot234° = 0
Without using trigonometric tables, prove that:
cos257° – sin233° = 0
Without using trigonometric tables, prove that:
sec250° – cot240° = 1
Without using trigonometric tables, prove that:
cosec272° – tan218° = 1
Without using trigonometric tables, prove that:
sin 32° cos 58° + cos 32° sin 58° = 1
Without using trigonometric tables, prove that:
cos 54° cos 36° – sin 54° sin 36° = 0
Without using trigonometric tables, prove that:
sec 70° sin 20° + cos 20° cosec 70° = 2
Without using trigonometric tables, prove that:
tan 15° tan 60° tan 75° = `sqrt(3)`
Without using trigonometric tables, prove that:
tan 48° tan 23° tan 42° tan 67° tan 45° = 1
Without using trigonometric tables, prove that:
(sin 72° + cos 18°)(sin 72° – cos 18°) = 0
Without using trigonometric tables, prove that:
cosec 39° cos 51° + tan 21° cot 69° – sec221° = 0
Express the following in terms of trigonometric ratios of angles between 0° and 45°.
sin 72° + cosec 72°
Express the following in terms of trigonometric ratios of angles between 0° and 45°.
cosec 66° + tan 66°
Express the following in terms of trigonometric ratios of angles between 0° and 45°.
tan 68° + sec 68°
Express the following in terms of trigonometric ratios of angles between 0° and 45°.
cot 59° + cosec 59°
Express the following in terms of trigonometric ratios of angles between 0° and 45°.
cos 51° + cot 49° – sec 47°
Express the following in terms of trigonometric ratios of angles between 0° and 45°.
sin 67° + cos 75°
If sin 3A = cos (A – 10°), where 3A is an acute angle then find ∠A.
If tan A = cot (A + 10°), where (A + 10°) is acute then find ∠A.
If cos 2A = sin (A – 15°), where 2A is acute then find ∠A.
If sec 4A = cosec (A – 15°), where 4A is acute then find ∠A.
If tan 2θ = cot (θ + 6º), where 2θ and (θ + 6º) are acute angles, find the value of θ.
If sin (θ + 36°) = cos θ, where (θ + 36°) is acute, find θ.
Without using trigonometric tables, find the value of the expression:
3 cot 31° tan 15° cot 27° tan 75° cot 63° cot 59°
Without using trigonometric tables, find the value of the expression:
`2((cos 58^circ)/(sin 32^circ)) - sqrt(3)((cos 38^circ "cosec" 52^circ)/(tan 15^circ tan 60^circ tan 75^circ))`
Without using trigonometric tables, find the value of the expression:
`{(cos 70^circ)/(sin 20^circ) + (cos 55^circ "cosec" 35^circ)/(tan 5^circ tan 25^circ tan 45^circ tan 65^circ tan 85^circ)}`
Without using trigonometric tables, find the value of the expression:
`{(sin^2 22^circ + sin^2 68^circ)/(cos^2 22^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin 27^circ}`
Without using trigonometric tables, find the value of the expression:
`{(cos 65^circ)/(sin 25^circ) + ("cosec" 34^circ)/(sec 56^circ) - (2 cos 43^circ "cosec" 47^circ)/(tan 10^circ tan 40^circ tan 50^circ tan 80^circ)}`
Without using trigonometric tables, find the value of the expression:
`cot θ tan (90^circ - θ) - sec (90^circ - θ)"cosec" θ + sin^2 65^circ + sin^2 25^circ + sqrt(3) tan 5^circ tan 45^circ tan 85^circ`
Without using trigonometric tables, find the value of the expression:
`(sec (90^circ - θ)"cosec" θ - tan (90^circ - θ)cot θ + cos^2 25^circ + cos^2 65^circ)/(3 tan 27^circ tan 63^circ)`
Without using trigonometric tables, find the value of the expression:
`(cos(90^circ - θ) sec(90^circ - θ) tan θ)/("cosec"(90^circ - θ)sin(90^circ - θ)cot(90^circ - θ)) + (tan(90^circ - θ))/(cot θ)`
Without using trigonometric tables, find the value of the expression:
sin (50° + θ) – cos (40° – θ) + tan 1° tan 10° tan 20° tan 70° tan 80° tan 89°
Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`.
R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० 12 Trigonometric Ratios of Some Complemantary Angles MULTIPLE-CHOICE QUESTIONS (MCQ) [Pages 593 - 594]
Choose the correct answer in each of the following questions:
`(sec 32^circ)/("cosec" 58^circ)` = ?
`2/3`
`16/29`
`16/3`
1
`(cos 12^circ)/(sin 78^circ) + (tan 23^circ)/(cot 67^circ)` = ?
0
1
2
`3/2`
tan 10° tan 15° tan 75° tan 80° = ?
`sqrt(3)`
1
`1/sqrt(3)`
–1
tan 5° tan 25° tan 30° tan 65° tan 85° = ?
1
`sqrt(3)`
`1/sqrt(3)`
`1/2`
cos 1° cos 2° cos 3°... cos 180° = ?
0
1
–1
`1/2`
sin 43° cos 47° + cos 43° sin 47° = ?
0
1
sin 4°
cos 4°
sec 70° sin 20° + cos 20° cosec 70° = ?
0
1
2
–2
cosec2 57° – tan2 33° = ?
1
0
–1
2
sec2 10° – cot2 80° = ?
0
1
`3/4`
`1/2`
`(2 sin^2 63^circ + 1 + 2 sin^2 27^circ)/(3 cos^2 17^circ - 2 + 3 cos^2 73^circ)` = ?
`2/3`
`3/2`
2
3
sin 38° – cos 52° = ?
0
1
`sqrt(3)/2`
`2/sqrt(3)`
`((sin^2 23^circ + sin^2 67^circ))/((cos^2 13^circ + cos^2 77^circ)) + sin^2 59^circ + cos 59^circ sin 21^circ` = ?
3
2
1
0
`((2 tan^2 30^circ sec^2 52^circ sin^2 38^circ)/("cosec"^2 70^circ - tan^2 20^circ))` = ?
2
1
`2/3`
`3/2`
`((cos 38^circ "cosec" 52^circ)/(tan 18^circ tan 35^circ tan 60^circ tan 72^circ tan 55^circ))` = ?
`1/3`
`1/sqrt(3)`
`sqrt(3)`
`2/sqrt(3)`
sin (60° + θ) – cos (30° – θ) = ?
2 sin θ
2 cos θ
0
1
If A and B are acute angles such that sin A = cos B then (A + B) = ?
30°
45°
60°
90°
If cos (α + β) = 0 then sin (α – β) = ?
sin 2α
cos 2β
sin α
cos β
sin (45° + θ) – cos (45° – θ) = ?
0
1
2
–2
If sec 4A = cosec (A – 10°) and 4A is acute then A = ?
20°
25°
30°
40°
If sin 3A = cos (A – 10°) and 3A is acute then A =?
15°
20°
25°
30°
Fill in the blanks.
cot 34° – tan 56° = .....
cosec 31° – sec 59° = ......
cos267° + cos223° = ......
cosec254° – tan236° = ......
sec240° – cot250° = ......
Solutions for 12: Trigonometric Ratios of Some Complemantary Angles
R.S. Aggarwal solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० chapter 12 - Trigonometric Ratios of Some Complemantary Angles
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