Question

Derive the trigonometric identity sin² theta + cos² theta = 1​

Answer 1

Answer:

sin²Ф+cos²Ф=1

Step-by-step explanation:

Draw a traingle ABC then take A as Ф and then side BC as opposite and side AB as adjacent and side AC is hypotenuse

   By pythagoras theorem,

         AC²=AB²+BC²

         AC²-AB²=BC²

         AC²-BC²=AB²

Ther are three possibilites

And now take only sinФ+cosФ

Here apply sinФ and cosФ formula that are opposite/hypotenuse for sinФ and adjacent/hypotenuse for cosФ

Here,

          sinФ+cosФ

       = (BC/AC)²+(AB/AC)²

       =BC²/AC²+AB²/AC²

Now we can take LCM,

      =BC²+AB²/AC²

Now we can see that there we solved three possibilities,we can take the first one that is AC²=AB²+BC²

We can take AC² in the place of AB²+BC²,

        =AC²/AC²

Both we can cancel now,

        =1

Hence it is proved.....

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