Ex 8.1 Class 10 Maths Question 3.
If sin A = 34 , calculate cos A and tan A.
Solution:
Ex 8.1 Class 10 Maths Question 4.
Given 15 cot A = 8, find sin A and sec A.
Solution:
Ex 8.1 Class 10 Maths Question 5.
Given sec θ = 1312 , calculate all other trigonometric ratios.
Solution:
Ex 8.1 Class 10 Maths Question 6.
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
Solution:
Ex 8.1 Class 10 Maths Question 7.
If cot θ = 78, evaluate:
(i) [Math Processing Error]
(ii) cot²θ
Solution:
Ex 8.1 Class 10 Maths Question 8.
If 3 cot A = 4, check whether [Math Processing Error] = cos² A – sin² A or not.
Solution:
Ex 8.1 Class 10 Maths Question 9.
In triangle ABC, right angled at B, if tan A = [Math Processing Error], find the value of:
(i) sin A cos C + cos A sin C
(ii) cos A cos C – sin A sin C
Solution:
Ex 8.1 Class 10 Maths Question 10.
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.
Solution:
Ex 8.1 Class 10 Maths Question 11.
State whether the following statements are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) sec A = [Math Processing Error] for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin θ = [Math Processing Error] for some angle.
Solution:
Class 10 Maths Introduction To Trigonometry
Trigonometry
Trigonometry is the study of relationships between the sides and angles of a right-angled triangle.
Trigonometric Ratios
Trigonometric ratios of an acute angle in a right triangle express the relationship between the angle and the length of its sides.
Let ∆ABC be a triangle right angled at B. Then the trigonometric ratios of the angle A in right ∆ABC are defined as follows:
Note:
The values of the trigonometric ratios of an angle do not vary with the lengths of the sides of the triangle, if the angle remains same.
Trigonometric Ratios for Complementary Angles
sin (90° – A) = cos A
cos (90° – A) = sin A
tan (90° – A) = cot A
cot (90° – A) = tan A
sec (90° – A) = cosec A
cosec (90° – A) = sec A
Note:
Here (90° – A) is the complementary angle of A.
Trigonometric Identities
An equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle(s) involved.
(i) sin2θ + cos2θ = 1 [for 0° ≤ θ ≤ 90°]
(ii) sec2θ – tan2θ = 1 [for 0° ≤ θ ≤ 90°]
(iii) cosec2θ – cot2θ = 1 [for 0° < θ ≤ 90°]
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