If sin calculate Cos A and tan A

NCERT - Mathematics

Book: NCERT - Mathematics

Chapter: 8. Introduction to Trigonometry

Subject: Maths - Class 10^th

Q. No. 3 of Exercise 8.1

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If sin calculate Cos A and tan A

Let ΔABC be a right-angled triangle, right-angled at point B

Given that,

Sin A =

Let BC be 3k. Therefore, AC will be 4k, where k is a positive integer.

Applying Pythagoras theorem in ΔABC, we obtain

AC² = AB² + BC²

(4k)² = AB² + (3k)²

16k² - 9k² = AB²

7k² = AB²

AB = k

Cos A =

= =

Tan A =

= =

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Chapter Exercises

Exercise 8.1

Exercise 8.2

Exercise 8.3

Exercise 8.4

Testing

1

In Δ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine:
(i) Sin A, Cos A

(ii) Sin C, Cos C

2

In Fig. 8.13, find tan P – cot R.

3

If sin calculate Cos A and tan A

4

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

5

Given sec calculate all other trigonometric ratios

6

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

7

If evaluate:
(i)

(ii)

8

If 3 cot A = 4, check whetheror not

9

In triangle ABC, right-angled at B, if find the value of:
(i) Sin A Cos C + Cos A Sin C

(ii) Cos A Cos C – Sin A Sin C

10

In Δ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of Sin P, Cos P and tan P

11

State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1

(ii) Secfor 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) for some angle θ