Question

plz attach answer on paper its urgent plz don't give wrong answer if you the I will also give wrong answer when you ask any question

Answer 1

$\sf \maltese \: \: \: { \underline{ \underline{Question \: : }}}$

• If sin⁴(x) + cos⁴(x) = 1+4k sin²(x) + cos²(x), then what is the value of k

$\sf \maltese \: \: \: { \underline{ \underline{Solution\: : }}}$

$\bull \: \: \: \: \: \sf{ \sin}^{4}(x) + { \cos}^{4} (x) = 1 + 4 \: k \: { \sin}^{2} (x) + { \cos}^{2} (x)$

$\sf \dashrightarrow \bigg({ \sin}^{2}(x) \bigg) ^{2} + \bigg( { \cos}^{2} (x) \bigg)^{2} = 1 + 4 \: k \: { \sin}^{2} (x) + { \cos}^{2} (x)$

$\sf \dashrightarrow \bigg( { \sin}^{2} (x) + { \cos}^{2} (x) \bigg) ^{2} - 2 \: \sin^{2} (x) \cos ^{2} (x) = 1 + 4 \: k \: { \sin}^{2} (x) + { \cos}^{2} (x)$

$\dashrightarrow \sf \cancel1 - 2 \: \sin^{2} (x) \cos ^{2} (x) = \cancel 1 + 4 \: k \: { \sin}^{2} (x) + { \cos}^{2} (x)$

$\dashrightarrow \sf \sin^{2} (x) \bigg(1 - \sin ^{2} (x) \bigg) = - 2 \: k \: { \sin}^{2} (x) + 1 - { \sin}^{2} (x)$

$\dashrightarrow \sf 2 \bigg( 1 + \: k \: \bigg) = \cosec ^{2} (x)+ \sin ^{2} (x)$

$\dashrightarrow \sf k \: = \frac{1}{2} \bigg( \cosec ^{2} (x)+ \sin ^{2} (x) \bigg) - 1$