Question

Sin²48° + sin²42° = 1

Answer 1

$\bold {Given:-} \begin{cases} \sf{LHS= {\sin }^{2} 48 \degree +{ \sin }^{2} 42 \degree} \\ \sf{RHS=1} \end {cases}$

$\large \underline {Solution:-</p><p>}$

${\sin }^{2} 48 \degree + { \sin }^{2}42 \degree = 1.$

Taking LHS:-

$= {\sin }^{2} 48 \degree + { \sin }^{2}42 \degree \\ \\ = { \sin }^{2} (90 - 48) + {\sin }^{2} 42 \degree \\ \\ = {\cos }^{2} 42 \degree + {\sin }^{2} 42 \degree \\ \\ = 1$

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Some Information :-

${ \sin }^{2} \phi +{ \cos }^{2} = 1. \\ \\ \sin(90 - \phi) = \cos \phi.$