Question

If A is an acute angle in a right triangle ABC, right angled at B, then the value of SinA+cosA is: (a) greater than one (b)equal to one (c)less than one (d)equal to two

Answer 1

A is an acute angle of right angle triangle ABC and right angled at B .
∴ A + B + C = 180°
A + 90° + C = 180°
A + C = 90°

Now, sinA + cosA
= √2{1/√2 sinA + 1/√2cosA}
= √2{cos45°.sinA + sin45°.cosA}
= √2sin(A + 45°)

Case 1:- when A = C
Then, A = C = 45° [ due to B is 90° ]
Then, √2sin(45°+45°) = √2 > 1

Case2 :- when A > C , like A = 15° and C = 75°
Then, √2sin(15° + 45°) = √2 × √3/2 = √3/√2 > 1

Case3:- when A < C , like A = 75° and C = 15°
Then, √2sin(75°+45°) = √3/√2 > 1

Hence, we observed in any cases value of sinA + cosA > 1
So, option ( a) is correct

Answer 2

Answer:

greater than 1

Step-by-step explanation:

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