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R.S. Aggarwal solutions for Class 10 Mathematics chapter 7 - Trigonometric Ratios of Complementary Angles

Secondary School Mathematics for Class 10 (for 2019 Examination)

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R.S. Aggarwal Secondary School Mathematics Class 10 (for 2019 Examination)

Secondary School Mathematics for Class 10 (for 2019 Examination) - Shaalaa.com

Chapter 7: Trigonometric Ratios of Complementary Angles

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Chapter 7: Trigonometric Ratios of Complementary Angles Exercise Exercise solutions [Pages 7 - 814]

Exercise | Q 1.1 | Page 312

Without using trigonometric tables, evaluate :
`sin 16^circ/cos 74^circ`

Exercise | Q 1.2 | Page 312

Without using trigonometric tables, evaluate :

`sec 11^circ/("cosec"  79^circ)`

Exercise | Q 1.3 | Page 312

Without using trigonometric tables, evaluate :

`tan 27^circ/cot 63^circ`

Exercise | Q 1.4 | Page 312

Without using trigonometric tables, evaluate :

`cos 35^circ/sin 55^circ`

Exercise | Q 1.5 | Page 312

Without using trigonometric tables, evaluate :

`("cosec"  42^circ)/sec 48^circ`

Exercise | Q 1.6 | Page 312

Without using trigonometric tables, evaluate :

`cot 38^circ/tan 52^circ`

Exercise | Q 2.1 | Page 312

Without using trigonometric tables, prove that:

cos 81° − sin 9° = 0

Exercise | Q 2.2 | Page 312

Without using trigonometric tables, prove that:

tan 71° − cot 19° = 0

Exercise | Q 2.3 | Page 312

Without using trigonometric tables, prove that:

cosec 80° − sec 10° = 0

Exercise | Q 2.4 | Page 312

Without using trigonometric tables, prove that:

cosec272° − tan218° = 1

Exercise | Q 2.5 | Page 312

Without using trigonometric tables, prove that:

cos275° + cos215° = 1

Exercise | Q 2.6 | Page 312

Without using trigonometric tables, prove that:

tan266° − cot224° = 0

Exercise | Q 2.7 | Page 312

Without using trigonometric tables, prove that:

sin248° + sin242° = 1

Exercise | Q 2.8 | Page 312

Without using trigonometric tables, prove that:

cos257° − sin233° = 0

Exercise | Q 2.9 | Page 312

Without using trigonometric tables, prove that:

(sin 65° + cos 25°)(sin 65° − cos 25°) = 0

Exercise | Q 3.1 | Page 313

Without using trigonometric tables, prove that:

sin53° cos37° + cos53° sin37° = 1

Exercise | Q 3.2 | Page 313

Without using trigonometric tables, prove that:

cos54° cos36° − sin54° sin36° = 0

Exercise | Q 3.3 | Page 313

Without using trigonometric tables, prove that:

sec70° sin20° + cos20° cosec70° = 2

Exercise | Q 3.4 | Page 313

Without using trigonometric tables, prove that:

sin35° sin55° − cos35° cos55° = 0

Exercise | Q 3.5 | Page 313

Without using trigonometric tables, prove that:

(sin72° + cos18°)(sin72° − cos18°) = 0

Exercise | Q 3.6 | Page 313

Without using trigonometric tables, prove that:

tan48° tan23° tan42° tan67° = 1

Exercise | Q 4.1 | Page 313

Prove that:

`(sin 70^circ)/(cos 20^circ) + ("cosec" 20^circ)/(sec 70^circ) - 2  cos 70^circ "cosec"  20^circ = 0`

Exercise | Q 4.2 | Page 313

Prove that:

`cos 80^circ/(sin 10^circ) + cos 59^circ "cosec"  31^circ = 2`

Exercise | Q 4.3 | Page 313

Prove that:

`(2  "sin"  68^circ)/(cos 10^circ )- (2  cot 15^circ)/(5 tan 75^circ) = ((3  tan 45^circ t  an 20^circ  tan 40^circ tan 50^circ tan 70^circ)) /5= 1` 

Exercise | Q 4.4 | Page 313

Prove that:

`sin 18^circ/(cos 72^circ )+ sqrt(3)(tan 10^circ tan 30^circ tan 40^circ  tan50^circ tan 80^circ) `

Exercise | Q 5.1 | Page 313

Prove that:

sin θ cos (90° - θ ) + sin (90° - θ) cos θ = 1

Exercise | Q 5.2 | Page 313

Prove that:

\[\frac{\sin\theta}{\cos(90° - \theta)} + \frac{\cos\theta}{\sin(90° - \theta)} = 2\]

Exercise | Q 5.3 | Page 313

Prove that:

\[\frac{\sin\theta  \cos(90^\circ - \theta)\cos\theta}{\sin(90^\circ- \theta)} + \frac{\cos\theta  \sin(90^\circ - \theta)\sin\theta}{\cos(90^\circ - \theta)}\]

Exercise | Q 5.4 | Page 313

Prove that:

\[\frac{sin\theta  \cos(90°  - \theta)cos\theta}{\sin(90° - \theta)} + \frac{cos\theta  \sin(90° - \theta)sin\theta}{\cos(90° - \theta)}\]

Exercise | Q 5.5 | Page 313

Prove that:

\[\frac{\cos(90^\circ - \theta)}{1 + \sin(90^\circ - \theta)} + \frac{1 + \sin(90^\circ- \theta)}{\cos(90^\circ - \theta)} = 2 cosec\theta\]

Exercise | Q 5.6 | Page 313

Prove that:

\[\frac{sin\theta  \cos(90° - \theta)cos\theta}{\sin(90° - \theta)} + \frac{cos\theta  \sin(90° - \theta)sin\theta}{\cos(90° - \theta)}\]

Exercise | Q 5.7 | Page 313

Prove that:

\[cot\theta \tan\left( 90° - \theta \right) - \sec\left( 90° - \theta \right)cosec\theta + \sqrt{3}\tan12° \tan60° \tan78° = 2\]

Exercise | Q 6.1 | Page 313

Prove that :

tan5° tan25° tan30° tan65° tan85° = \[\frac{1}{\sqrt{3}}\]

Exercise | Q 6.2 | Page 313

Prove that:

cot12° cot38° cot52° cot60° cot78° = \[\frac{1}{\sqrt{3}}\]

Exercise | Q 6.3 | Page 313

Prove that:

cos15° cos35° cosec55° cos60° cosec75° = \[\frac{1}{2}\]

Exercise | Q 6.4 | Page 313

Prove that:

cos1° cos2° cos3° ... cos180° = 0

Exercise | Q 6.5 | Page 313

Prove that:

\[\left( \frac{\sin49^\circ}{\cos41^\circ} \right)^2 + \left( \frac{\cos41^\circ}{\sin49^\circ} \right)^2 = 2\]

Exercise | Q 7.1 | Page 314

Prove that

sin (70° + θ) − cos (20° − θ) = 0

Exercise | Q 7.2 | Page 314

Prove that

tan (55° − θ) − cot (35° + θ) = 0

Exercise | Q 7.3 | Page 314

Prove that

cosec (67° + θ) − sec (23° − θ) = 0

Exercise | Q 7.4 | Page 314

Prove that

 cosec (65 °+ θ)  sec  (25° −  θ) − tan (55° − θ) + cot (35° + θ) = 0

Exercise | Q 7.5 | Page 314

Prove that

sin (50° + θ ) − cos (40° − θ) + tan 1° tan 10° tan 80° tan 89° = 1.

Exercise | Q 8.1 | Page 314

Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.

sin67° + cos75° 

Exercise | Q 8.2 | Page 314

Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.

cot65° + tan49°

Exercise | Q 8.3 | Page 814

Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.

sec78° + cosec56°

Exercise | Q 8.4 | Page 314

Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.

cosec54° + sin72°

Exercise | Q 9 | Page 314

If A, B  and C are the angles of a  ΔABC, prove that tan `((C + "A")/2) = cot  B/2`

Exercise | Q 10 | Page 7

If cos 20 = sin 4 θ ,where 2 θ and 4 θ are acute angles, then find the value of θ

Exercise | Q 11 | Page 314

If sec2A = cosec(A - 42°), where 2A is an acute angle, then find the value of A.  

Q 12 | Page 314

If sin 3 A = cos (A − 26°), where 3 A is an acute angle, find the value of A.

Exercise | Q 13 | Page 314

If tan 2 A = cot (A − 12°), where 2 A is an acute angle, find the value of A.

Exercise | Q 14 | Page 314

If sec 4 A = cosec (A − 15°), where 4 A is an acute angle, find the value of A.

Exercise | Q 15 | Page 314
\[\frac{2}{3} {cosec}^2 58^\circ- \frac{2}{3}\cot58^\circ \tan32^\circ - \frac{5}{3}\tan13^\circ \tan37^\circ\tan45^\circ\tan53^\circ\tan77^\circ = - 1\]

Chapter 7: Trigonometric Ratios of Complementary Angles

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R.S. Aggarwal Secondary School Mathematics Class 10 (for 2019 Examination)

Secondary School Mathematics for Class 10 (for 2019 Examination) - Shaalaa.com

R.S. Aggarwal solutions for Class 10 Mathematics chapter 7 - Trigonometric Ratios of Complementary Angles

R.S. Aggarwal solutions for Class 10 Maths chapter 7 (Trigonometric Ratios of Complementary Angles) 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 CBSE Secondary School Mathematics for Class 10 (for 2019 Examination) solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. R.S. Aggarwal textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 7 Trigonometric Ratios of Complementary Angles are Introduction to Trigonometry, Introduction to Trigonometry Examples and Solutions, Trigonometric Ratios, Trigonometric Ratios of an Acute Angle of a Right-angled Triangle, Trigonometric Ratios of Some Specific Angles, Trigonometric Ratios of Complementary Angles, Trigonometric Identities, Proof of Existence, Relationships Between the Ratios.

Using R.S. Aggarwal Class 10 solutions Trigonometric Ratios of Complementary Angles exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in R.S. Aggarwal Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer R.S. Aggarwal Textbook Solutions to score more in exam.

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