Question

Derivation of trigonometric identities using complex numbers

Answer 1

Sin = p/h
Cos = b/h

square if sin & cos and adding both

= p²/h² + b²/h²

= p²+b² / h² [ by Pythagoras theorem ]

= h²/h² = 1

So , sin²@ + cos²@ = 1 -----( i )


Now divide this eq(i) by sin²@

we get ,

1 + cos²/sin²@ = 1 / sin²@

1 + cot²@ = cosec²@ ------( ii )

Now , divide eq ( i ) by cos²@

we get ,

sin²@ / cos²@ + 1 = 1 / cos2@

tan²@ + 1 = sec²@ -------( iii )


By eq ( i ) , ( ii ) , ( iii ) we get trigonometry identities .


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