Question

Prove that Cos⁴teta - Cos²theta = Sin⁴teta - Sin²theta

Answer 1

Hiii friend,


Cos^4 theta - Cos² theta = Sin^4 - Sin²theta

LHS = Cos^4 theta - Cos² theta


=> Cos² theta (Cos² theta-1)


=> (1-Sin²theta) (-Sin²theta)


=> -Sin²theta + Sin^4 theta



=> Sin^4 theta - Sin²theta = RHS.


HENCE,


LHS = RHS...... PROVED......


HOPE IT WILL HELP YOU...... :-)

Answer 2

$let \: theta \: be \: \alpha \\ given - - > {cos}^{4} \alpha - {cos}^{2} \alpha = {sin}^{4} \alpha - {sin}^{2} \alpha \\ solving \: lhs - - > {cos}^{4} \alpha - {cos}^{2} \alpha \\ = > {cos}^{2} \alpha ( {cos}^{2} \alpha - 1) \\ = > {cos}^{2} \alpha ( - {sin}^{2} \alpha ) \\ = > - {sin}^{2} \alpha {cos}^{2} \alpha \\ now \: solving \: rhs - - > {sin}^{4} \alpha - {sin}^{2} \alpha \\ = > {sin}^{2} \alpha ( {sin}^{2} \alpha - 1) \\ = > {sin}^{2} \alpha ( - {cos}^{2} \alpha ) \\ = > - {sin}^{2} \alpha {cos}^{2} \alpha \\ \\ = > lhs \: = \: rhs \\ \\ hence \: proved$