Reduce each of the following expressions to the Sine And Cosine ofA single expression: cos x – sin x

RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 7. Values of Trigonometric Functions at Sum of Difference of Angles

Subject: Maths - Class 10^th

Q. No. 2 of Exercise 7.2

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2

Reduce each of the following expressions to the Sine And Cosine ofA single expression:
cos x – sin x

Let f(x) = cos x – sin x

Dividing and multiplying by √(1 + 1) = √2,

Sine of expression:

We know that sinA cosB – cosA sinB = sin(A –B)

Cosine of the expression:

We know that cosA cosB – sinA sinB = cos(A +B)

2

Chapter Exercises

Exercise 7.1

Exercise 7.2

Very Short Answer

MCQ

1

Find the maximum and minimum values of each of the following trigonometrical expressions:
(i) 12 sin x- 5 cos x

(ii) 12 cos x + 5 sin x+ 4

(iii)

(iv) sin x – cos x + 1

2

Reduce each of the following expressions to the Sine And Cosine of A single expression:

2

Reduce each of the following expressions to the Sine And Cosine ofA single expression:
cos x – sin x

2

Reduce each of the following expressions to the Sine And Cosine ofA single expression:
24 cos x + 7 sin x

3

Show that Sin 100⁰ – Sin 10⁰ is positive.

4

Prove that lies between and .