Math, asked by ridhimagulati916, 9 months ago

Please prove the question in the given pic

Attachments:

Answers

Answered by saurabhsemalti
1

Answer:

proved

Step-by-step explanation:

taking RHS

2( {cos}^{4}  \alpha  + sin {}^{4}  \alpha ) ....(1)\\ we \: can \: write \\{cos}^{4}  \alpha  + sin {}^{4}  \alpha \: as \\ ( {cos}^{2}  \alpha  +  {sin}^{2}  \alpha ) {}^{2}  - 2( {cos}^{2}  \alpha sin {}^{2}  \alpha ) \\  = (1) {}^{2}  - 2( {cos}^{2}  \alpha sin {}^{2}  \alpha ) \\ putting \: in \: (1) \\  = 2(1 - 2 {cos}^{2} \alpha  sin {}^{2}  \alpha ) \\  = 2 - 4 {cos}^{2} \alpha  sin {}^{2}  \alpha  \\  = 2 - (2 {sin}^{ \alpha }  \cos( \alpha ) ) {}^{2}  \\  = 2 -  {sin}^{2} (2 \alpha )...(2) \\ we \: know \\ sin {}^{2}  (2\alpha) +  cos {}^{2}(2  \alpha ) = 1 \\  {sin}^{2} (2 \alpha ) = 1 - (cos {}^{2} (2 \alpha )) \\ putting \: in \: (2) \\  = 2 - ( {sin}^{2} 2 \alpha )\\ =  2 - (1 -  {cos}^{2} 2 \alpha ) \\  = 1 +  {cos}^{2} 2 \alpha

mark as brainliest if helped

Similar questions