Question

Prove that sin4a+2sin2acos2a+cos4a=1 ​

Answer 1

`\qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star`

`\textsf{ \underline{\underline{Steps to solve the problem} }:}`

`\qquad❖ \: \sf \: \sin {}^(4) ( \alpha) + 2 \sin {}^(2) ( \alpha) \cos {}^(2) ( \alpha) + { \cos {}^(4) ( \alpha) }^{}`

`\qquad❖ \: \sf \:( \sin {}^(2) ( \alpha) ) {}^(2) + 2( \sin {}^(2) ( \alpha))( \cos {}^(2) ( \alpha)) + {( \cos {}^(2) ( \alpha)) }^{}`

( use identity a² + 2ab + b² = (a + b)² )

`\qquad❖ \: \sf \:( {\sin {}^(2)( { \alpha}) + \cos {}^(2) ( \alpha)) }^(2)`

( sin² x + cos ² x = 1 )

`\qquad❖ \: \sf \: {1}^(2)`

`\qquad❖ \: \sf \: {1}^{}`

`\qquad \large \sf {Conclusion} :`

Value of that expression is 1