# If Sin (A + B) = 1 and Cos (A – B) = 1, 00 ≤ (A + B) ≤ 900 and a > B, Then Find a and B. - Mathematics

If sin (A + B) = 1 and cos (A – B) = 1, 0 ≤ (A + B) ≤ 900  and A > B, then find A and B.

#### Solution

Here, sin (A + B) = 1
⇒ sin (A + B) = 90            [∵ sin 900 = 1]
⇒ (A + B) = 900                               …….(i)
Also, cos (A – B) = 1
⇒ cos (A – B) = 00                [∵ cos 00 = 1]
⇒ A – B = 00                                   ….(ii)
Solving (i) and (ii), we get:
A = 450 and B = 45

Concept: Trigonometric Ratios and Its Reciprocal
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 6 T-Ratios of some particular angles
Exercises | Q 23
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