Question

2sin^2theta +7cos theta =5
then Find value of cos theta​

Answer 1

Answer:

$2 {sin}^{2} \theta \: + 7cos \theta = 5 \\ 2(1 - {cos}^{2} \theta )+ 7cos \theta - 5 = 0 \\ 2 - 2 {cos}^{2} \theta + 7cos \theta - 5 = 0 \\ - 2 {cos}^{2} \theta + 7cos \theta - 3 = 0 \\ 2 {cos}^{2} \theta - 7cos \theta + 3 = 0 \\ 2 {cos}^{2} \theta - 6cos \theta - cos \theta + 3 = 0 \\ 2cos \theta(cos \theta - 3) - 1(cos \theta - 3) = 0 \\ (cos \theta - 3)(2cos \theta - 1) = 0 \\ cos \theta - 3 = 0 \: or \: 2cos \theta - 1 = 0 \\\fbox { cos \theta = 3 \: \: \: or \: \: \: cos \theta = \frac{1}{2} } \\ \\ \\ \because \: maximum \: value \: of \: cos \: is \: 1. \\ \cos \theta \neq \: 3 \\ hence \\ cos \theta = \frac{1}{2} \implies \: cos \theta =cos \: 60 \degree \\ \theta \: =60 \degree$

Answer 2

Step-by-step explanation:

hope it is help for you. sorry for direct hundriting.