RD Sharma - Mathematics

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


Chapter Exercises

More Exercise Questions

6

If SinA = 1/2, cosB = , where π/2<A < π And 0 <B < π/2, find the following:

(i) tan(A +B)(ii) tan(A -B)