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

KSEEB SSLC Class 10 Maths Solutions Chapter 11 Introduction to Trigonometry Ex 11.1 are part of KSEEB SSLC Class 10 Maths Solutions. Here we have given Karnataka SSLC Class 10 Maths Solutions Chapter 11 Introduction to Trigonometry Exercise 11.1.

Karnataka SSLC Class 10 Maths Solutions Chapter 11 Introduction to Trigonometry Exercise 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:
Trigonometry Exercise 11.1 Solutions KSEEB
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 KSEEB

Introduction To Trigonometry Class 10 Exercise 11.1 Question 2.
In the given figure, find tan P – cot R.
Solution:
Introduction To Trigonometry Exercise 11.1 KSEEB
In ⊥∆PQR, ∠Q = 90°
∴ PQ2 + QR2 = PR2
(12)2 + QR2 = (13)2
144 + QR2 = 169
QR2 = 169 – 144
QR2 = 25
∴ QR = 5 cm.
Exercise 11.1 Class 10 Trigonometry KSEEB

Introduction To Trigonometry Exercise 11.1 Question 3.
If sin A = \(\frac{3}{4}\) calculate cos A and tan A.
Solution:
KSEEB Solutions For Class 10 Maths Trigonometry
10th Maths Introduction To Trigonometry Exercise 11.1 KSEEB

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

KSEEB Solutions For Class 10 Maths Trigonometry Question 5.
Given sec θ = \(\frac{13}{12}\), calculate all other trigonometric ratios
Solution;
Trigonometry Class 10 Exercise 11.1 KSEEB

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.
Introduction To Trigonometry Class 10 KSEEB
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 = \(\frac{7}{8}\), evaluate :
(i) \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\)
(ii) cot2θ
Solution:
Trigonometry Ex 11.1 KSEEB
10th Class Trigonometry Exercise 11.1 KSEEB

Trigonometry Class 10 Exercise 11.1 Question 8.
If 3 cot A = 4, check whether \(\frac{1-\tan ^{2} A}{1+\tan ^{2} A}\) = cos2 A – sin2 A or not
Solution:
Introduction Of Trigonometry Exercise 11.1 KSEEB
KSEEB Solutions For Class 10 Maths Introduction To Trigonometry

Introduction To Trigonometry Class 10 KSEEB Question 9.
In ∆ABC, right-angled at B, if tan A =\(\frac{1}{\sqrt{3}}\) find the value of:
i) sin A cos C + cos A sin C
ii) cos A cos C – sin A sin C
Solution:
Trigonometry Exercise 11.1 KSEEB
Trigonometry Lesson Exercise 11.1 KSEEB

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
10th Class Maths Trigonometry Chapter Exercise 11.1 KSEEB
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
10 Maths Trigonometry 11.1 KSEEB

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° = \(\sqrt{3}\) > 1

(ii) If sec A = \(\frac{12}{5}\) 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 = \(\frac{\text { Adjacent side }}{\text { Opposite side }}\)

(v) sin θ = \(\frac{4}{3}\) for some angle θ
Answer:
False. because sin θ ≯ 1

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