RD Sharma - Mathematics

Book: RD Sharma - Mathematics

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

Subject: - Class 11th

Q. No. 24 of Exercise 7.1

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24

If lies in the first quadrant And cos x = 8/17, then prove that

Given x lies in the first quadrant i.e. 0 < x < π/2 And cos x = 8/17


We know that



LHS


= cos(30 + x) + cos(45 – x) + cos(120 – x)


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


= cos 30° cos x – sin 30° sin x + cos 45° cos x + sin 45° sin x + cos 120° cos x + sin 120° sin x


= cos x(cos 30° + cos 45° + cos 120°) + sin x(-sin 30° + sin 45° + sin 120°)





= RHS


Hence, proved.


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)