Question

Sin^6A-cos^6A=(2sin^2A-1)(cos^2Asin^4A)

Answer 1

Answer:

$\red { sin^{6}A - cos^{6}A}\green {= (2sin^{2}A-1)(sin^{4}A + cos^{2}A)}$

Step-by-step explanation:

$LHS \red { = sin^{6}A - cos^{6}A}$

$= (sin^{2})^{3}A - (cos^{2})^{3}A$

$= (sin^{2}A - cos^{2}A)[(sin^{2})^{2}+sin^{2}A cos^{2} A + (cos^{2}A)^{2}]$

$\boxed {\pink { x^{3}-y^{3} = (x-y)(x^{2}+xy+y^{2})}}$

$= [sin^{2}A-(1-sin^{2}A)][sin^{4}A+sin^{2}A cos^{2} A + cos^{4} A]$

$= (sin^{2}A - 1+sin^{2}A) [sin^{4}A+cos^{2}A(sin^{2}A+cos^{2}A]$

$\green {= (2sin^{2}A-1)(sin^{4}A + cos^{2}A)}$

$\boxed { \pink { sin^{2}A + cos^{2}A = 1}}$

$= RHS$

Therefore.,

$\red { sin^{6}A - cos^{6}A}\green {= (2sin^{2}A-1)(sin^{4}A + cos^{2}A)}$

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