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