Question

if sin A = cos B then prove that A+B=90°​

Answer 1

Step-by-step explanation:

sina = p/h

sinB= b/h

since sinA= sinB

therefore ,p/h=b/h

therefore h cancelled

si p=h

and, we know that if two sides of a right triangle is equal then is a isosceles right triangle

therefore angle A + angle b is equals to 90 degre.

since angle a is equal to angle bis equals to 45°

hence proved

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Answer 2

Answer:

1. A = B = 45 degree

2. 0

3. 1

Step-by-step explanation:

1. METHOD 1

sin45 = cos45

So, A = B = 45 degree

METHOD 2

sinA = p/h

sinB= b/h

Since sinA= sinB  

Therefore, p/h=b/h

Therefore h is cancelled,    p=h

and, we know that if two sides of a right triangle is equal then is a isosceles right triangle.

Therefore angle A + angle b is equals to 90 degree.

Since angle a is equal to angle bis equals to 45°.

2. cos36cos54 - sin36sin54              [sinA = cos(90-A)]

=> cos36sin36 - sin36cos36 = 0

3. sin5cos85 + cos5sin85

=> cos85cos85 + sin85sin85

=> cos²85 + sin²85                             [sin²A + cos²A = 1]

=> 1

Hope this helps.....