RD Sharma - Mathematics

Book: RD Sharma - Mathematics

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

Subject: - Class 11th

Q. No. 22 of Exercise 7.1

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22

If CosA + SinB = m And SinA + CosB = n, prove that 2 Sin(A +B) = m2 + n2 – 2.

Given cosA + sinB = m And sinA + cosB = n


RHS = m2 + n2 – 2


=(cosA + sinB)2 +(sinA + cosB)2 – 2


= cos2A + sin2B + 2 cosA sinB + sin2A + cos2B + 2 sinA cosB – 2


= 1 + 1 + 2(cosA sinB + sinA cosB) - 2


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


= 2 sin(A +B)


= LHS


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)