# PSEB Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.1

PSEB Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.1

## PSEB 10th Class Maths Solutions Chapter 8 Introduction to Trigonometry Ex 8.1

Question 1.

In ∆ABC, right angled at B, AB = 24 cm; BC = 7 cm. Determine

(i) sin A, cos A

(ii) sin C, cos C.

Solution:

(i) We are to find sin A .cos A AB = 24 cm; BC = 7 cm

By using Pythagoras Theorem,

Question 4.

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

Solution:

Let ABC be any right angled triangle where A is an acute angle with right angle at B.

Question 6.

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

Solution:

Let ABC be any triangle, where ∠A and ∠B are acute angles. To find cos A and cos B.

Question 10.

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

Solution:

Given: ∆PQR, right angled at Q

PR + QR = 25 cm

PQ = 5 cm

In right angled triangle PQR

By using Pythagoras Theorem,

(PR)^{2} = (PQ)^{2} + (RQ)^{2}

or (PR)^{2} = (5)^{2} + (RQ)^{2}

[∴ PR + QR = 25, QR = 25 – PR]

or (PR)^{2} = 25 + [25 – PR]^{2}

or (PR)^{2} = 25 + (25)^{2} + (PR)^{2} – 2 × 25 × PR

or (PR)^{2} = 25 + 625 + (PR)^{2} – 50

or (PR)^{2} – (PR)^{2} + 50 PR = 650

or 50 PR = 650

or PR = 650/50

or PR = 13 cm

QR = 25 – PR

QR = (25 – 13) cm

or QR = 12 cm.

Question 11.

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

(i) The value of tan A is always less than 1

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

(iii) cos A is abbreviation used for cosecant of angle A.

(iv) cot A is product of cot and A.

(v) sin θ = 4/3 for some angle θ.

Solution:

(i) False

∵ tan 60° = √3 = 1.732 > 1.

(ii) True; sec A = 12/5 = 240 > 1

∵ Sec A is always greater than 1.

(iii) False.

Because cos A is used for cosine A.

(iv) False.

Because cot A is cotangent of the angle A not the product of cot and A.

(v) False; sin θ = 4/3 = 1.666 > 1

Because sin θ is always less than 1.

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