Ncert solutions mathematics class 10 Solutions for Chapter 8 introduction to trigonometry

Exercises in Chapter 8 introduction to trigonometry Grade 10

Introduction to Trigonometry - Exercise 8.1

Introduction to Trigonometry - Exercise 8.2

Introduction to Trigonometry - Exercise 8.3

Introduction to Trigonometry - Exercise 8.4

Questions in Introduction to Trigonometry - Exercise 8.1

Given sec θ = 13/12 Find tan θ.

Given sec θ = 13/12 Find cot θ.

In triangle ABC, right-angled at B, if tan A = $\frac{1}{\sqrt{3}}$ find the value of cos A cos C + sin A sin C.

Given 15 cot A = 8, find sin A and sec A.

Given sec θ = 13/12 Find cos θ.

State whether the following statment is true or false.

cot A is the product of cot and A

In ∆ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P.

State whether the following statment is true or false.

sin θ = 4/3 for some angle θ.

State whether the following statment is true or false.

cos A is the abbreviation used for the cosecant of angle A.

In triangle ABC, right-angled at B, if tan A = $\frac{1}{\sqrt{3}}$ find the value of sin A cos C + cos A sin C.

If $\sin\theta=\frac{4}{5}$ , then find the value of $\frac{4\sinθ-\cos\theta+1}{4\sinθ+\cos\theta-1}$

If $\tan\theta=\frac{a}{b}$ , then find the value of $\frac{\cos\theta+\sin\theta}{\cos\theta-\sin\theta}$

In ∆ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of cos P.

In ∆ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P.

State whether the following statment is true or false.

The value of tan A is always less than 1.

State whether the following statment is true or false.

$secA=\frac{12}{5}$ for some value of angle A.

In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine sin C, cos C

In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm and AC = 25 cm. Determine the value of cos A

In Fig, find tan P – cot R

If sin A = 3/4, Calculate cos A and tan A.

Given sec θ = 13/12 Find sin θ.

Given sec θ = 13/12 Find cosec θ.

If ∠A and ∠B are acute angles such that cos A = cos B, check if ∠ A = ∠ B.

If cot θ = 7/8, evaluate cot² θ.

If cot θ = 7/8, evaluate $\frac{(1 + sin θ)(1 – sin θ)}{(1+cos θ)(1-cos θ)}$

If 3 cot A = 4, check whether $\frac{1-\tan ^{2} \mathrm{~A}}{1+\tan ^{2} \mathrm{~A}}=cos ^{2} \mathrm{~A}-\sin ^{2} \mathrm{~A}$ or not.**

Questions in Introduction to Trigonometry - Exercise 8.2

$\frac{2\tan30^{\circ}}{1-\tan^230^{\circ}}=$

Evaluate sin 60° cos 30° + sin 30° cos 60°.

$\frac{2\tan30^{\circ}}{1+\tan^230^{\circ}}\ =$

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

Evaluate $\frac{\sin30^{\circ}+\tan45^{\circ}-\operatorname{cosec}60^{\circ}}{\sec30^{\circ}+\cos60^{\circ}+\cot45^{\circ}}$

$\frac{1-\tan ^{2} 45^{\circ}}{1+\tan ^{2} 45^{\circ}}=$

State whether the following statment is true or false.

The value of sin θ increases as θ increases.

State whether the following statment is true or false.

The value of cos θ increases as θ increases.

If tan A = cot B, check if A + B = 90°.

State whether true or false:

tan 48° tan 23° tan 42° tan 67° = 1

If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.

Evaluate cosec 31° – sec 59°.

If A, B and C are interior angles of a triangle ABC, state whether $\sin (\frac{B+C}{2}) = \cos \frac{A}{2}$

9 sec²A – 9 tan²A =

Evaluate: $2\sec^260°+\cot^230°-\operatorname{cosec}^230°$

If $\tan\alpha=\sqrt{3}$ and $\tan\beta=\frac{1}{\sqrt{3}}$ 0° < ⍺, β < 90°, find the value of $\cot\left(\alpha+\beta\right)$ .

Find the value of (1 + cot A – cosec A) (1 + tan A + sec A).

If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.

Evaluate 2 tan² 45° + cos² 30° – sin² 60.

Evaluate $\frac{\cos 45^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}}$

Evaluate $\frac{5\cos^260^{\circ}+4\sec^230^{\circ}-\tan^245^{\circ}}{\sin^230^{\circ}+\cos^230^{\circ}}$

sin 2A = 2 sin A is true when A =

State whether the following statment is true or false.

sin (A + B) = sin A + sin B.

State whether the following statment is true or false.

sin θ = cos θ for all values of θ.

State whether the following statment is true or false.

cot A is not defined for A = 0°.

Evaluate $\frac{\sin 18°}{\cos 72°}$

Evaluate $\frac{\tan 26°}{\cot 64°}$

Evaluate cos 48° – sin 42°.

State whether true or false:

cos 38° cos 52° – sin 38° sin 52° = 0

(sec A + tan A) (1 – sin A) =

Find the value of $\frac{1+\tan^2A}{1+\cot^2A}$ .

Questions in Introduction to Trigonometry - Exercise 8.3

How sin 67° + cos 75° is expressed in terms of trigonometric ratios of angles between 0° and 45°?

Questions in Introduction to Trigonometry - Exercise 8.4

State whether L.H.S and R.H.S are equal:

$(\cosec θ – \cot θ)^2= \frac{(1-\cos θ)}{(1+\cos θ)}$

State whether L.H.S and R.H.S are equal:

$\frac{\cos A-\sin A+1}{\cos A+\sin A-1}=\operatorname{cosec}A+\cot A$

Express (sin A + cosec A)²+ (cos A + sec A)² in terms of

$\tan^2A$ and $\cot^2A$ .

State whether L.H.S and R.H.S are equal:

$\sqrt{\frac{1+\sin\mathrm{A}}{1-\sin\mathrm{A}}}=\sec\mathrm{A}+\tan\mathrm{A}$

Express the trigonometric ratio of tan A in terms of cot A.

Write the trigonometric ratios of sin A in terms of sec A.

Evaluate $\frac{\sin^263+\sin^227^{\circ}}{\cos^217^{\circ}+\cos^273^{\circ}}$

Evaluate sin 25° cos 65° + cos 25° sin 65°

Write the trigonometric ratios of cos A in terms of sec A.

Write the trigonometric ratios of tan A in terms of sec A.

Write the trigonometric ratios of cosec A in terms of sec A.

Write the other trigonometric ratios of cot A in terms of sec A.

Find the value of $\frac{\sin\theta-2\sin^3\theta}{2\cos^3\theta-\cos\theta}$ .

State whether L.H.S and R.H.S are equal:

$\frac{\tan \theta}{1-\cot \theta}+\frac{\cot \theta}{1-\tan \theta}=1+\sec \theta \operatorname{cosec} \theta$

State whether L.H.S and R.H.S are equal:

$\frac{1+\sec\mathrm{A}}{\sec\mathrm{A}}=\frac{\sin^2\mathrm{~A}}{1-\cos\mathrm{A}}$

State whether L.H.S and R.H.S are equal:

$(\operatorname{cosec}A-\sin A)(\sec A-\cos A)=\frac{1}{\tan A+\cot A}\ \ \ \ \ \ \ ...[1]$

Express the trigonometric ratio of sin A in terms of cot A.

State whether L.H.S and R.H.S are equal:

$\left(\frac{1+\tan^2A}{1+\cot^2A}\right)=\left(\frac{1-\tan A}{1-\cot A}\right)^2$

State whether L.H.S and R.H.S are equal:

$\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}=2 \sec A$

Express the trigonometric ratio of sec A in terms of cot A.

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Chapters in this book

Real Numbers

Polynomials

Pair of Linear Equations in Two Variables

Quadratic Equations

Arithmetic Progressions

Triangles

Coordinate Geometry

Introduction to Trigonometry

Some Applications of Trigonometry

Circles

Areas Related to Circles

Surface Areas and Volumes

Statistics

Probability