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

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

Exercises
Exercises

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

Exercises | Q 1

Evaluate:
sin600 cos300 + cos600 sin300

Exercises | Q 2

Evaluate:
cos600 cos300− sin600 sin300

Exercises | Q 3

Evaluate:
cos450 cos300 + sin450 sin300

Exercises | Q 4

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

Exercises | Q 5

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

Exercises | Q 6

Evaluate:

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

Exercises | Q 7

Evaluate:

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

Exercises | Q 8

Evaluate:

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

Exercises | Q 9

Evaluate:

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

Exercises | Q 10.1

Show that:

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

Exercises | Q 10.2

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

Exercises | Q 11.1

Verify each of the following:

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

Exercises | Q 11.2

Verify each of the following:

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

Exercises | Q 11.3

Verify each of the following:

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

Exercises | Q 11.4

Verify each of the following:

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

Exercises | Q 12.1

If A = 450, verify that :
(i) sin 2A = 2 sin A cos A

Exercises | Q 12.2

If A = 45, verify that:

(ii) cos 2A = 2 cos2 A – 1 = 1 – 2 sin2

Exercises | Q 13.1

If A = 30, verify that:

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

Exercises | Q 13.2

If A = 30, verify that:

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

Exercises | Q 13.3

If A = 30, verify that:

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

Exercises | Q 14.1

If A = 600 and B = 300, verify that:
(i) sin (A + B) = sin A cos B + cos A sin B

Exercises | Q 14.2

If A = 600 and B = 300, verify that:

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

Exercises | Q 15.1

If A = 600 and B = 300, verify that:
(i) sin (A – B) = sin A cos B – cos A sin B

Exercises | Q 15.2

If A = 600 and B = 300, verify that:

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

Exercises | Q 15.3

If A = 600 and B = 300, verify that:

(iii) tan (A-B) = (tan A-tanB)/(1+tan A tan B)

Exercises | Q 16

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

Exercises | Q 17

Using the formula, tan 2A =(2 tan A )/(1- tan^2 A) find the value of tan 600, it being given that tan 300 = 1/sqrt(3).

Exercises | Q 18

Using the formula, cos A = sqrt((1+cos2A)/2) ,find the value of cos 300, it being given that cos 600  = 1/2.

Exercises | Q 19

Using the formula, sin A = sqrt((1-cos 2A)/2)  find the value of sin 300, it being given that cos 600 = 1/2

Exercises | Q 20

In the adjoining figure, ΔABC is a right-angled triangle in which ∠B = 900, ∠300 and AC = 20cm. Find (i) BC, (ii) AB.

Exercises | Q 21

In the adjoining figure, ΔABC is right-angled at B and ∠A = 300. If  BC = 6cm, find (i) AB, (ii) AC.

Exercises | Q 22

In the adjoining figure, ΔABC is right-angled at B and ∠A = 450. If AC = 3sqrt(2)cm, find (i) BC, (ii) AB.

Exercises | Q 23

If sin (A + B) = 1 and cos (A – B) = 1, 0 ≤ (A + B) ≤ 900  and A > B, then find A and B.

Exercises | Q 24

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.

Exercises | Q 25

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.

Exercises | Q 26

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

Exercises | Q 27

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 (750)
(ii) cos (150

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

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

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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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