Question

Prove that sin2thita +cos2thita =1

Answer 1

Answer:

cos = b/h and sin = b/h

LHS

Sin2 +cos2

={p/h}2 +[b/h]2

=p2 +b2 /h2

=h2/h2

=1

=RHS.......{...HENCE PROVED}

Explanation:

Please adjust with figure

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Answer 2

Considering the question is asked for sin²Ф+cos²Ф=1 and not for sin2Ф+cos2Ф=1 because no such formula exists so

For figure of ΔABC you can refer to attachment

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Given; ΔABC in which AB⊥BC

To Prove; sin²Ф+cos²Ф=1

Proof;

In a ΔABC

We know that

sinФ=Perpendicular÷hypotenuse=BC÷AC -----------------(1)                                    

cosФ=Base÷hypotenuse=AB÷AC              ------------------ (2)

Squaring and adding equation 1 and equation 2

sin²Ф+cos²Ф=AB²+BC²/AC²

Now, by pythagoras theorem

Perpendicular²+Base²=Hypotenuse²

So here, AB²+BC²=AC²

sin²Ф+cos²Ф=AC²/AC²

sin²Ф+cos²Ф=1

LHS=RHS

Hence Proved

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