Question

if sinA=cosB prove A+B=90°​

Answer 1

SinA=CosB prove A+B=90

Sin(90°-A)=CosB

Cos(90π-A)=CosB

90°- A=B

A+B=90°

Answer 2

$</p><p>\Rightarrow \qquad \sin{A} = \cos{B} \\ \\ \Rightarrow \qquad \sin{A} = \cos(90-B) \\ \\ \Rightarrow \qquad \sin{A} = \sin{90-B} \qquad [ \sin{\theta} = \cos(90-\theta) ] \\ \\ \Rightarrow \qquad A = 90 - B \\ \\ \Rightarrow \qquad A + B = 90° \\ \\ \boxed{\bold{Hence, Proved}}</p><p>$