Question

(b) cosec A- sin A= m and sec A - cos A = n then eliminate A​

Answer 1

Step-by-step explanation:

$given \: \csc(a) - \sin(a) = m \\ we \: know \: that \: \csc(a) = \frac{1}{sin(a)} \\ so \: \frac{1}{ \sin(a) } - \sin(a) = m \\ take \: lcm \\ \frac{1 - sin {}^{2}(a) }{sin(a)} \\ and \: 1 - sin {}^{2} (a) = cos {}^{2} (a) \\ and \: \frac{cos {}^{2} (a)}{sin(a)} = m - - - - - - - -(1)$

$\sec(a) - \cos(a) = n \\ we \: know \: that \: sec(a) = \frac{1}{cos(a)} \\ and \: \frac{1}{ \cos(a) } - cos(a) = n \\ so \: \frac{1 - cos {}^{2}(a) }{cos(a)} = n \\ and \: \: \: \frac{sin {}^{2} (a)}{cos(a)} = n - - - - - -( 2)$

$and \: sin {}^{2} (a) + cos {}^{2} (a) = 1 \\ we \: can \: write \: as \: \\ (sin {}^{3} (a)) {}^{ \frac{2}{3} } \\ so \: it \: is \: evaluated$