Question

If 7 cosec^2 theta-9 cot^2theta=7 then what is the value of tantheta​

Answer 1

`\displaystyle\\Answer:\theta=(\pi )/(2)+\pi n.`

Explanation:

`\displaystyle\\7*cosec^2\theta-9*cot^2\theta=7\\7-7*cosec^2\theta+9*cot^2\theta=0\\7-(7)/(sin^2\theta)+9*(cos^2\theta)/(sin^2\theta) } =0\\(7*sin^2\theta-7+9*cos^2\theta)/(sin^2\theta) =0\\(-7*(1-sin^2\theta)+9*cos^2\theta)/(sin^2\theta) =0\\(-7*cos^2\theta+9*cos^2\theta)/(sin^2\theta) =0\\(2*cos^2\theta)/(sin^2\theta)=0\\`

`2*cot^2\theta=0\\Divide\ the\ right\ and\ initial\ parts\ by\ 2:\\cot^2\theta=0\\cot\theta=0\\\theta=(\pi )/(2)+\pi n\ \ \ (n=0,\ 1,\ 2,\ 3\ ...).`