Question

Given sec A = 2 Find the value of
(sin^3 A + cos^3 A)/(sin A + cos A) +
(sin^3 A - cos^3 A)/(sin A - cos A)​

Answer 1

step by step explanation:

Answer 2

Answer:

2

Step-by-step explanation:

$\frac{sin {}^{3 }a + cos {}^{3}a }{sin \: a \: + \: cos \: a} + \frac{sin {}^{3 }a - cos {}^{3}a }{sin \: a \: - \: cos \: a}$

$\frac{(sin {}^{3}a + cos {}^{3}a)(sin \: a \: - \: cos \: a) \: + \: (sin {}^{3}a - cos {}^{3}a)(sin \: a \: + \: cos \: a)} {(sin \: a{} + \: cos \: a)( sin \: a{} - \: cos \: a) }$

$\frac{2(sin {}^{4} - cos {}^{4}) }{sin {}^{2}a \: - \: cos {}^{2}a }$

$\frac{2(sin {}^{2}a + cos {}^{2} a) (sin {}^{2}a - cos {}^{2} a)}{sin {}^{2} a - cos {}^{2} a}$

2(sin²a+cos²a)

= 2(1)

= 2