Question

in a right angle triangle ABC right angled at p square of the hypotenuse is equal to twice the product of the other two sides show that Sin A is equals to Cos A​

Answer 1

Answer:

∠A=∠C=45°

Step-by-step explanation:

Consider AB=a , BC=b , CA=c ;

Given : c²=2ab ;

Using pythagoras theorem ,

c²=a²+b² ;

Substitue c²,

∴ a²+b² = 2ab;

∴ a²+b²-2ab = 0;

∴ (a-b)² = 0;

∴ a=b;

∴ It is an isosceles right angled triangle.

∴ ∠A = 45° .

∴ As  sinA = 1/√2  and  cosA=1/√2

∴ Sin A= Cos A  .