R s aggarwal solutions mathematics class 10 Solutions for Chapter 7 t ratios of some particular angles

Exercises in Chapter 7 t ratios of some particular angles Grade 10

T-Ratios Of Some Particular Angles Exercise 11

Questions in T-Ratios Of Some Particular Angles Exercise 11

Evaluate:

$\sin 60^{\circ} \cos 30^{\circ}+\cos 60^{\circ} \sin 30^{\circ}$

Evaluate:

cos 60° cos 30° − sin 60° sin 30°.

Evaluate:

cos 45° cos 30° + sin 45° sin 30°.

Evaluate:

$\frac{\sin 30^{\circ}}{\cos 45^{\circ}}+\frac{\cot 45^{\circ}}{\sec 60^{\circ}}-\frac{\sin 60^{\circ}}{\tan 45^{\circ}}+\frac{\cos 30^{\circ}}{\sin 90^{\circ}}$

Evaluate:

$\left(5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}\right) /\left(\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}\right)$

Evaluate:

$2 \cos ^{2} 60^{\circ}+3 \sin ^{2} 45^{\circ}-3 \sin ^{2} 30^{\circ}+2 \cos ^{2} 90^{\circ}$

Evaluate:

$\cot ^{2} 30^{\circ}-2 \cos ^{2} 30^{\circ}-3 / 4 \sec ^{2} 45^{\circ}+1 / 4 \operatorname{cosec}^{2} 30^{\circ}$

Evaluate:

$\left(\sin ^{2} 30^{\circ}+4 \cot ^{2} 45^{\circ}-\sec ^{2} 60^{\circ}\right)\left(\operatorname{cosec}^{2} 45^{\circ} \sec ^{2} 30^{\circ}\right)$

Evaluate:

$4 / \cot ^{2} 30^{\circ}+1 / \sin ^{2} 30^{\circ}-2 \cos ^{2} 45^{\circ}-\sin ^{2} 0^{\circ}$

Show that:

$\text { (i) } \frac{1-\sin 60^{\circ}}{\cos 60^{\circ}}=\frac{\tan 60^{\circ}-1}{\tan 60^{\circ}+1}$

$\text { (ii) } \frac{\cos 30^{\circ}+\sin 60^{\circ}}{1+\sin 30^{\circ}+\cos 60^{\circ}}=\cos 30^{\circ}$

Verify each of the following:

(i) sin 60° cos 30° − cos 60° sin 30° = sin 30°

(ii) cos 60° cos 30° + sin 60° sin 30° = cos 30°

(iii) 2 sin 30° cos 30° = sin 60°

(iv) 2 sin 45° cos 45° = sin 90°

If A = 45°, verify that:

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

$\text { (ii) } \cos 2 A=2 \cos ^{2} A-1=1-2 \sin ^{2} A$

If A = 30°, verify that:

$\text { (i) } \sin 2 A=\frac{2 \tan A}{1-\tan ^{2} A}$

$\text { (ii) } \cos 2 A=\frac{1-\tan ^{2} A}{1+\tan ^{2} A}$

$\text { (iii) } \tan 2 A=\frac{2 \tan A}{1-\tan ^{2} A}$

If A = 60° and B = 30°, verify that:

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

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

If A = 60° and B = 30°, verify that:

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

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

$\text { (iii) } \tan (A-B)=\frac{\tan A-\tan B}{1+\tan A \tan B}$

If A and B are acute angles such that tan A = 1/3, tan B = 1/2 and

$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}$

Show that A + B = 45°.

Using the formula,

$\tan 2 A=\frac{2 \tan A}{1-\tan ^{2} A}$

find the value of tan 60°, it being given that tan 30° = 1/√3.

Using the formula,

$\cos A=\sqrt{\frac{1+\cos 2 A}{2}}$

find the value of cos 30°, it being given that cos 60° = 1/2.

Using the formula,

$\sin A=\sqrt{\frac{1-\cos 2 A}{2}}$

find the value of sin 30°, it being given that cos 60° = 1/2.

In the adjoining figure, ∆ABC is a right-angled triangle in which ∠B = 90°, ∠A = 30° and AC = 20 cm.

Find (i) BC, (ii) AB.

In the adjoining figure, ∆ ABC is a right-angled at B and ∠A = 30°. If BC = 6 cm,

Find (i) AB, (ii) AC.

If sin (A + B) = 1 and cos (A − B) = 1, 0° ≤ (A + B) ≤ 90° and A > B, then find A and B.

If sin (A − B) = 1/2 and cos (A + B) = 1/2, 0° < (A + B) < 90° and A > B, then find A and B.

If tan (A − B) = 1/√3 and tan (A + B) = √3, 0° < (A + B) < 90° and A > B, then find A and B.

If 3x = cosec θ and 3/x = cot θ, find the value of 3(x^2 – 1/x^2).

If sin(A+B) = sinA cosB+cosA sinB and cos(A-B)=cosA cosB+sinA sinB,

find the values of (i) sin75° and (ii) cos15°.

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Chapters in this book

Real Numbers

Coordinate Geometry

Triangles

Circles

Constructions

Trigonometric Ratios

T-Ratios Of Some Particular Angles

Trigonometric Ratios Of Complementary Angles

Trigonometric Identities

Height And Distance

Perimeter And Area Of Plane Figures

Area Of Circle Sector And Segment