Express the trigonometric ratios sin A, sec A and tan A in terms of cot A

NCERT - Mathematics

Book: NCERT - Mathematics

Chapter: 8. Introduction to Trigonometry

Subject: Maths - Class 10^th

Q. No. 1 of Exercise 8.4

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1

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A

sinA can be expressed in terms of cotA as:

1/(√cosec²A)

= 1/√(1 + cot²A)

Now,

Sec can be expressed in terms of cot A as:

secA = √sec²A

= √(1 + tan²A)

= √[1 + (1/cot²A)]

= √[(1 + cot²A)/cot²A]

= [√(1 + cot²A)]/cotA

And,

TanA can be expressed in terms of cotA as:

tanA =

3

Chapter Exercises

Exercise 8.1

Exercise 8.2

Exercise 8.3

Exercise 8.4

Testing

1

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A

2

Write all the other trigonometric ratios of ∠ A in terms of sec A

3

Evaluate:

(i)

(ii) Sin 25° Cos 65° + Cos 25° Sin 65°

4

Choose the correct option. Justify your choice.

4

Choose the correct option. Justify your choice.

4

Choose the correct option. Justify your choice.
(Sec A + tan A) (1 – sin A) =

4

Choose the correct option. Justify your choice.

5

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

(i)

(ii)

(iii)

(iv)

(v) using the identity

(vi)

(vii)

(viii)

(ix) [Hint: Simplify LHS and RHS separately]

(x)