Question

A+B=90° Prove that Sin square A + cos square B =1​

Answer 1

Answer:

Given, A + B = 90°

To prove :- Sin²A + Cos²A = 1

Proof :-

Let ABC be a right angled triangle at B and its perpendicular, base and hypotenuse be represented by P, B & H

SinA = P/H, CosA = B/H

By squaring and adding the values of SinA and CosA we get,

Sin²A + Cos²A = P²/H² + B²/H²

= P² + B²/ H²

= H²/H² ( By pythagoras theorem)

= 1

LHS = RHS (Hence proved)

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