Question

If $7cosec\phi -3cot\phi =7$, then $7cot\phi -3cosec\phi =$

Answer 1

$7cosec\phi -3cot\phi =7$ .......... (1)

$7cot\phi -3cosec\phi =x$.......... (2)

Adding (1) and (2), we get

$4cosec\phi +4cot\phi =7+x$

$cosec\phi +cot\phi =\frac{7+x}{4}$.......... (3)

Subtracting (2) from (1), we get

$10cosec\phi -10cot\phi =7-x$

$cosec\phi -cot\phi =\frac{7-x}{10}$.......... (4)

Multiply (3) and (4),

$cose{c}^2\phi -co{t}^2\phi =\frac{49-x^2}{40}$

$1=\frac{49-x^2}{40}$

$x^2=49-40=9$

$x=\pm 3$