## Book: RD Sharma - Mathematics

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

#### Subject: - Class 11th

##### Q. No. 7 of Exercise 7.1

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7
##### Evaluate the following:(i) sin 780 cos 180 – cos 780 sin 180 (ii) cos 470 cos 130 - sin 470 sin 130(iii) sin 360 cos 90 + cos 360 sin 90 (iv) cos 800 cos 200 + sin 800 sin 200

(i) Given sin 780 cos 180 – cos 780 sin 180

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

sin 780 cos 180 – cos 780 sin 180 = sin(78 – 18) °

= sin 60°

(ii) Given cos 470 cos 130 - sin 470 sin 130

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

cos 470 cos 130 - sin 470 sin 130 = cos(47 + 13) °

= cos 60°

= 1/2

cos 470 cos 130 - sin 470 sin 130 = 1/2

(iii) Given sin 360 cos 90 + cos 360 sin 90

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

sin 360 cos 90 + cos 360 sin 90 = sin(36 + 9) °

= sin 45°

(iv) Given cos 800 cos 200 + sin 800 sin 200

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

cos 800 cos 200 + sin 800 sin 200 = cos(80 - 20) °

= cos 60°

= 1/2

cos 800 cos 200 + sin 800 sin 200 = 1/2

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