sin-x-cos-x-1-proof-by-step-by-step-or-by-showing-all-steps-b-c-it-is-my-assignment-

Question Number 129634 by abdurehime last updated on 17/Jan/21

{s i n}^{} x + {c o s}^{} x = 1 proof by step by step or by showing all steps

b / c it is my assignment

Answered by MJS_new last updated on 17/Jan/21

the easiest way to prove is graphically .

{here}^{'} s a different proof :

\sin x = \frac{e^{i x} - e^{- i x}}{2 i} \land \cos x = \frac{e^{i x} + e^{- i x}}{2}

let e^{i x} = p

\sin^{2} x + \cos^{2} x = \frac{{(p - \frac{1}{p})}^{2}}{{(2 i)}^{2}} + \frac{{(p + \frac{1}{p})}^{2}}{2^{2}} =

= \frac{p^{2} - 2 + \frac{1}{p^{2}}}{- 4} + \frac{p^{2} + 2 + \frac{1}{p^{2}}}{4} = \frac{4}{4} = 1

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