Question

plsss give the answer... if 7sin^2theta + 3cos^2theta = 4 then sec theta + cosec thehta==???

Answer 1

Let theta be a.
So,
$7 { \sin }^{2} a \: + 3 { \cos }^{2}a = 4 \\ = > 7(1 - { \cos }^{2} a) + 3 { \cos }^{2} a = 4 \\ = > 7 - 7 { \cos }^{2} a + 3 { \cos}^{2} a = 4 \\ = > - 4 { \cos }^{2} a = - 3 \\ = > { \cos }^{2} a = \frac{3}{4} \\ = > \cos \: a = \frac{ \sqrt{3} }{2} \\ = > \cos \: a = \cos \: 30° \\ => a = 30° \\ \sec \: a + \csc \: a = \sec \: 30° + \csc \: 30° \\ = \frac{2}{ \sqrt{3} } + 2 = \frac{2 \sqrt{3} }{3} + 2 \\ = \frac{2 \sqrt{3} + 6}{3}$