Question

prove that
cos⁴theta - cos² theta = sin⁴theta - sin² theta ​

Answer 1

Answer:

samjh me na aay to fir se puchh Lena Bata dunga

Answer 2

TO PROVE :–

$\\ \sf \to \: { \cos}^{4} ( \theta) - { \cos}^{2}( \theta) = { \sin}^{4} ( \theta) - { \sin}^{2}( \theta)$

SOLUTION :–

• Let's take L.H.S. –

$\\ \sf \: \: = \: \: { \cos}^{4} ( \theta) - { \cos}^{2}( \theta)$

• We know that –

$\\ \sf \: \implies \: { \sin}^{2} ( \theta) + { \cos}^{2}( \theta) = 1$

• So that –

$\\ \sf \: \: = \: \: {[1 - { \sin}^{2}( \theta) ]}^{2} - [1 - { \sin}^{2}( \theta) ]$

$\\ \sf \: \: = \: \: 1 + { \sin}^{4} ( \theta) - 2 { \sin}^{2}( \theta) - 1 + { \sin}^{2}( \theta)$

$\\ \sf \: \: = \: \: { \sin}^{4} ( \theta) - 2 { \sin}^{2}( \theta) + { \sin}^{2}( \theta)$

$\\ \sf \: \: = \: \: { \sin}^{4} ( \theta) + { \sin}^{2}( \theta) [1 - 2]$

$\\ \sf \: \: = \: \: { \sin}^{4} ( \theta) + { \sin}^{2}( \theta) [ - 1]$

$\\ \sf \: \: = \: \: { \sin}^{4} ( \theta) - { \sin}^{2}( \theta)$

$\\ \sf \: \: = \: \: R.H.S.$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large { \overbrace{ \underbrace{ \sf \: Hence \: \: proved \: }}}$

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