NCERT solutions for Class 10 Maths chapter 8 - Introduction to Trigonometry [Latest edition]

In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine

sin A, cos A

In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine sin C, cos C

 In Given Figure, find tan P – cot R.

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

Given 15 cot A = 8. Find sin A and sec A

Given sec θ = `13/12` , calculate all other trigonometric ratios.

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

If cot θ = 7/8 evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`

If cot θ = 7/8, evaluate cot² θ

If 3 cot A = 4, Check whether `((1-tan^2 A)/(1+tan^2 A)) = cos^2 A - sin^2 A` or not

In ΔABC, right angled at B. If tan A = `1/sqrt3` , find the value of

(i) sin A cos C + cos A sin C

(ii) cos A cos C − sin A sin C

In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

State whether the following are true or false. Justify your answer.

The value of tan A is always less than 1.

State whether the following are true or false. Justify your answer.

sec A = 12/5 for some value of angle A.

State whether the following are true or false. Justify your answer.

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

State whether the following are true or false. Justify your answer. cot A is the product of cot and A

State whether the following are true or false. Justify your answer.

sin θ =4/3, for some angle θ

Evaluate the following in the simplest form: sin 60º cos 30º + cos 60º sin 30º

Evaluate the following : 2tan²45° + cos²30° − sin²60°

Evaluate the following : `(cos 45°)/(sec 30° + cosec 30°)`

Evaluate the following

`(sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°)`

Evaluate the following

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

Choose the correct option and justify your choice

`(2 tan 30°)/(1+tan^2 30°)`

Choose the correct option and justify your choice.

`(1- tan^2 45°)/(1+tan^2 45°) `

Choose the correct option and justify your choice :

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

Choose the correct option and justify your choice :

`(2 tan 30°)/(1-tan^2 30°)`

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

State whether the following is true or false. Justify your answer.

sin (A + B) = sin A + sin B

State whether the following is true or false. Justify your answer.

The value of sinθ increases as θ increases

State whether the following is true or false. Justify your answer.

The value of cos θ increases as θ increases

State whether the following is true or false. Justify your answer

sinθ = cos θ for all values of θ

State whether the following are true or false. Justify your answer.

cot A is not defined for A = 0°

Evaluate `(sin 18^@)/(cos 72^@)`

Evaluate `(tan 26^@)/(cot 64^@)`

Evaluate cos 48° − sin 42°

Evaluate cosec 31° − sec 59°

Show that tan 48° tan 23° tan 42° tan 67° = 1

Show that cos 38° cos 52° − sin 38° sin 52° = 0

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

If tan A = cot B, prove that A + B = 90

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

If A, B and C are interior angles of a triangle ABC, then show that `\sin( \frac{B+C}{2} )=\cos \frac{A}{2}`

Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

Write all the other trigonometric ratios of ∠A in terms of sec A.

Evaluate

`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`

 Evaluate sin25° cos65° + cos25° sin65°

Choose the correct option. Justify your choice.

9 sec² A − 9 tan² A =

Choose the correct option. Justify your choice.

(1 + tan θ + sec θ) (1 + cot θ − cosec θ)

Choose the correct option. Justify your choice.

(secA + tanA) (1 − sinA) =

Choose the correct option. Justify your choice.

`(1+tan^2A)/(1+cot^2A)`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined

`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined

`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined

`(tantheta)/(1-cottheta) + (cottheta)/(1-tantheta) = 1+secthetacosectheta`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

`(1+ secA)/sec A = (sin^2A)/(1-cosA)`

[Hint : Simplify LHS and RHS separately]

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

`sqrt((1+sinA)/(1-sinA)) = secA + tanA`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined

`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
(sin A + cosec A)² + (cos A + sec A)² = 7 + tan² A + cot² A

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
(cosec A – sin A) (sec A – cos A)`=1/(tanA+cotA)`

[Hint : Simplify LHS and RHS separately]

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

`((1+tan^2A)/(1+cot^2A))=((1-tanA)/(1-cotA))^2=tan^2A`