KSEEB SSLC Class 10 Maths Solutions Chapter 11 Introduction to Trigonometry Ex 11.1

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Karnataka State Syllabus Class 10 Maths Solutions Chapter 11 Introduction to Trigonometry Ex 11.1

Trigonometry Exercise 11.1 Solutions 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:

In ⊥∆ABC, ∠B = 90°
As per Pythagoras theorem
AC² = AB² + BC²
= (24)² + (7) ²
= 576 + 49
AC² = 625
∴ AC = 25 cm

Introduction To Trigonometry Class 10 Exercise 11.1 Question 2.
In the given figure, find tan P – cot R.
Solution:

In ⊥∆PQR, ∠Q = 90°
∴ PQ² + QR² = PR²
(12)² + QR² = (13)²
144 + QR² = 169
QR² = 169 – 144
QR² = 25
∴ QR = 5 cm.

Introduction To Trigonometry Exercise 11.1 Question 3.
If sin A = 34 calculate cos A and tan A.
Solution:

Exercise 11.1 Class 10 Trigonometry Question 4.
Given 15 cot A = 8, find sin A and sec A.
Solution:

KSEEB Solutions For Class 10 Maths Trigonometry Question 5.
Given sec θ = 1312, calculate all other trigonometric ratios
Solution;

10th Maths Introduction To Trigonometry Exercise 11.1 Question 6.
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
Solution:
In ⊥∆ABC, ∠A and ∠B are acute angles. CD ⊥ AB is drawn.

CD is common.
S.S.S. Postulate :
∴ ∆ADC ~ ∆ADB
∴ ∠A = ∠B
∵ “Angles of similar triangles are equiangular.”

10th Class Maths Trigonometry Exercise 11.1 Question 7.
If cot θ = 78, evaluate :
(i) (1+sinθ)(1−sinθ)(1+cosθ)(1−cosθ)
(ii) cot²θ
Solution:

Trigonometry Class 10 Exercise 11.1 Question 8.
If 3 cot A = 4, check whether 1−tan2A1+tan2A = cos² A – sin² A or not
Solution:

Introduction To Trigonometry Class 10 KSEEB Question 9.
In ∆ABC, right-angled at B, if tan A =13√ find the value of:
i) sin A cos C + cos A sin C
ii) cos A cos C – sin A sin C
Solution:

Trigonometry Ex 11.1 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:
PQ = 5 cm
PR + QR = 25 cm
∴ PR = 25 – QR

PR² = PQ² + QR²
QR² = PR² – PQ²
= (25 – QR)² – (5)²
QR² = 625 – 50QR + QR² – 25
50QR = 600
∴ QR = 12 cm.
∴ PR = 25 – QR = 25 – 12 = 13 cm.
∴ QR = 12 cm
∴ PR = 25 – QR = 25 – 12 = 13 cm

10th Class Trigonometry Exercise 11.1 Question 11.
State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
Answer:
False. 60° = 3–√ > 1

(ii) If sec A = 125 for some value of angle A.
Answer:
True. because sec A > 1.

(iii) cos A is the abbreviation used for the cosecant of angle A.
Answer:
False. Because cos A is simplified as cos.

(iv) cot A is the product of cot and A.
Answer:
False. cot is ∠A or meaningless. Here,
cot A =  Adjacent side  Opposite side 

(v) sin θ = 43 for some angle θ
Answer:
False. because sin θ ≯ 1

All Chapter KSEEB Solutions For Class 10 Maths

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All Subject KSEEB Solutions For Class 10

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