Question

prove that (sinø + cosø)² = 1+sin2ø​

Answer 1

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${( \sin \phi + \cos \phi)}^{2} = 1 + {\sin}^{2} \phi$

Let's take LHS try to prove RHS.

$\rightarrow{ \sin}^{2} \phi + {\cos }^{2} \phi + 2 \sin \phi. \cos \phi \\ \\ \rightarrow 1 + 2 \sin \phi. \cos \phi \\ \\ \rightarrow \: 1 + sin \: 2 \phi$

${Hence\:\: proved}$

${ \underline{ \underline{ \star \: some \: formual}}}$

${ \sin}^{2} \phi + { \cos}^{2}\phi = 1. \\ \\ \sin \: 2 \phi = 2 \sin \phi. \cos \phi.$

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