Question

if 2 sin^2θ+7 cosθ=5 then find the permissible values of cos θ

Answer 1

Answer:

$\cos( \alpha ) = \frac{ - 2}{ - 4} = \frac{1}{2}$

Step-by-step explanation:

$2 { \sin( \alpha ) }^{2} + 7 \cos( \alpha ) = 5 \\ \\ 2(1 - { \cos( \alpha ) }^{2} ) + 7 \cos( \alpha ) = 5 \\ \\ 2 - 2 { \cos( \alpha ) }^{2} + 7 \cos( \alpha ) = 5 \\ \\ \\ \\ - 2 { \cos( \alpha ) }^{2} + 7 \cos( \alpha ) - 3 = 0 \\ \\ \\ d = {7}^{2} - 4(2)(3) \\ \\ d = 49 - 24 \\ \\ d = 25 \\ \\ \sqrt{d} = 5 \\ \\ \cos( \alpha ) = \frac{ - 7 + 5}{2 \times - 2} \\ \\ \\ \cos( \alpha ) = \frac{ - 2}{ - 4} = \frac{1}{2}$