#### Online Mock Tests

#### 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

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

Below listed, you can find solutions for Chapter 6 of CBSE RS Aggarwal for Secondary School Class 10 Maths.

### RS Aggarwal solutions for Secondary School Class 10 Maths Chapter 6 T-Ratios of some particular angles Exercises

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^circ + 4 sec^2 30^circ - tan^2 45^circ)/(sin^2 30^circ + cos^2 30^circ)`

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) = `sqrt3` and tan (A – B) = `1/sqrt3` ; 0° < A + B ≤ 90° ; A > B, 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})

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

## RS Aggarwal solutions for Secondary School Class 10 Maths chapter 6 - T-Ratios of some particular angles

Shaalaa.com has the CBSE Mathematics Secondary School Class 10 Maths CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. RS Aggarwal solutions for Mathematics Secondary School Class 10 Maths CBSE 6 (T-Ratios of some particular angles) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

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Concepts covered in Secondary School Class 10 Maths chapter 6 T-Ratios of some particular angles are Trigonometry, Trigonometric Ratios, Trigonometric Ratios of Some Special Angles, Trigonometric Ratios of Complementary Angles, Trigonometric Identities, Proof of Existence, Relationships Between the Ratios, Trigonometry, Trigonometric Ratios and Its Reciprocal, Trigonometry, Trigonometric Ratios, Trigonometric Ratios of Some Special Angles, Trigonometric Ratios of Complementary Angles, Trigonometric Identities, Proof of Existence, Relationships Between the Ratios, Trigonometry, Trigonometric Ratios and Its Reciprocal.

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