Question

Geometrically prove that sin²Ф+cos²Ф=1 .( No absurd answers please)

Answer 1

Step-by-step explanation:

Considering the question is asked for sin?0+cos?Q=1 and not for sin 20+cos20=1 because no such formula exists so

For figure of AABC you can refer to attachment

Given; AABC in which ABIBC To Prove; sin?Q+cos?Q=1

Proof;

In a ДАВС

We know that

sino=Perpendicular=hypotenuse=BC=AC ---(1)

cosO=Base-hypotenuse=AB÷AC

(2)

Squaring and adding equation 1 and equation 2

sin?@+cos?Q=AB2-BC2/AC2

Now, by pythagoras theorem

Perpendicular?+Base?=Hypotenuse?

So here, AB?+BC²=AC?

sin?Q+cos?Q=AC/AC2

sin?Q+cos?Q=1

LHS=RHS

Hence Proved

Answer 2

Step-by-step explanation:

this is proved that left hand side = right hand side