#### Chapters

Chapter 2: Polynomials

Chapter 3: Linear Equations in two variables

Chapter 4: Triangles

Chapter 5: Trigonometric Ratios

Chapter 6: T-Ratios of some particular angles

Chapter 7: Trigonometric Ratios of Complementary Angles

Chapter 8: Trigonometric Identities

Chapter 9: Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

Chapter 10: Quadratic Equations

Chapter 11: Arithmetic Progression

Chapter 12: Circles

Chapter 13: Constructions

Chapter 14: Height and Distance

Chapter 15: Probability

Chapter 16: Coordinate Geomentry

Chapter 17: Perimeter and Areas of Plane Figures

Chapter 18: Area of Circle, Sector and Segment

Chapter 19: Volume and Surface Area of Solids

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

## Chapter 6: T-Ratios of some particular angles

#### Chapter 6: T-Ratios of some particular angles solutions [Page 0]

Evaluate:

sin60^{0} cos30^{0} + cos60^{0} sin30^{0}

Evaluate:

cos60^{0} cos30^{0}− sin60^{0} sin30^{0}

Evaluate:

cos45^{0} cos30^{0} + sin45^{0} sin30^{0}

Evaluate:

`(sin30°)/(cos 45°)+(cot45°)/(sec60° )- (sin60°)/(tan45°)+(cos30°)/(sin90°)`

Evaluate:

`(5 cos^2 60^0 + 4 sec^2 30^0 -tan^2 45^0)/(sin^2 30^0+cos^2 30^0)`

Evaluate:

`2cos^2 60^0+3 sin^2 45^0 - 3 sin^2 30^0 + 2 cos^2 90 ^0`

Evaluate:

`cot^2 30^0-2cos^2 30^0-3/4 sec^2 45^0 +1/4 cosec^2 30^0`

Evaluate:

`(sin^2 30^0 + 4 cot^2 45^0-sec^2 60^0)(cosec^2 45^0 sec^2 30^0)`

Evaluate:

`4/(cot^2 30^0) +1/(sin^2 30^0) -2 cos^2 45^0 - sin^2 0^0`

Show that:

(i)` (1-sin 60^0)/(cos 60^0)=(tan60^0-1)/(tan60^0+1)`

Show that:

(ii) `(cos30^0+sin 60^0)/(1+sin30^0+cos60^0)=cos 30^0`

Verify each of the following:

(i)`sin 60^0 cos 30^0-cos 60^0 sin 30^0`

Verify each of the following:

(ii)`cos 60^0 cos 30^0+ sin 60^0 sin30^0`

Verify each of the following:

(iii) `2 sin 30^0 cos 30^0`

Verify each of the following:

(iv) `2 sin 45^0 cos 45^0`

If A = 45^{0}, verify that :

(i) sin 2A = 2 sin A cos A

If A = 45^{0 }, verify that:

(ii) cos 2A = 2 cos^{2} A – 1 = 1 – 2 sin^{2} A

If A = 30^{0 }, verify that:

(i) sin 2A = `(2 tan A)/(1+tan^2A)`

If A = 30^{0 }, verify that:

(ii) cos 2A = `(1- tan^2A)/(1+tan^2A)`

If A = 30^{0 }, verify that:

(iii) tan 2A = `(2tanA)/(1-tan^2A)`

If A = 60^{0} and B = 30^{0}, verify that:

(i) sin (A + B) = sin A cos B + cos A sin B

If A = 60^{0} and B = 30^{0}, verify that:

cos (A + B) = cos A cos B - sin A sin B

If A = 60^{0} and B = 30^{0}, verify that:

(i) sin (A – B) = sin A cos B – cos A sin B

If A = 60^{0} and B = 30^{0}, verify that:

(ii) cos (A – B) = cos A cos B + sin A sin B

If A = 60^{0} and B = 30^{0}, verify that:

(iii) tan (A-B) = `(tan A-tanB)/(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) =` show that `A+B = 45^0`

Using the formula, tan 2A =`(2 tan A )/(1- tan^2 A)` find the value of tan 60^{0}, it being given that tan 30^{0} = `1/sqrt(3)`.

Using the formula, cos A = `sqrt((1+cos2A)/2) ,`find the value of cos 30^{0}, it being given that cos 60^{0} = `1/2`.

Using the formula, sin A = `sqrt((1-cos 2A)/2) ` find the value of sin 30^{0}, it being given that cos 60^{0} = `1/2`

In the adjoining figure, ΔABC is a right-angled triangle in which ∠B = 90^{0}, ∠30^{0} and AC = 20cm. Find (i) BC, (ii) AB.

In the adjoining figure, ΔABC is right-angled at B and ∠A = 30^{0}. If BC = 6cm, find (i) AB, (ii) AC.

In the adjoining figure, ΔABC is right-angled at B and ∠A = 45^{0}. If AC = 3`sqrt(2)`cm, find (i) BC, (ii) AB.

If sin (A + B) = 1 and cos (A – B) = 1, 0^{0 } ≤ (A + B) ≤ 90^{0} and A > B, then find A and B.

If sin (A – B) = `1/2` and cos (A + B) = `1/2, 0^0 ≤ (A + B) ≤ 90^0` and A > B, then find A and B.

If tan (A – B) = `1/sqrt(3) and tan (A + B) = sqrt(3), 0^0 ≤ (A + B) ≤ 90^0 and A > B`, then find A and B.

If 3x = cosecθ = and `3/x= cottheta` find the value of 3`(x^2-1/x^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

(i) sin (75^{0})

(ii) cos (15^{0})

## Chapter 6: T-Ratios of some particular angles

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

#### Textbook solutions for Class 10

## R.S. Aggarwal solutions for Class 10 Mathematics chapter 6 - T-Ratios of some particular angles

R.S. Aggarwal solutions for Class 10 Maths chapter 6 (T-Ratios of some particular 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.

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Concepts covered in Class 10 Mathematics chapter 6 T-Ratios of some particular 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.

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