Question

if cosectheta+cottheta=k then find value of cos theta in terms of k

Answer 1

heya●

Cosec¢+cot¢=k

=)1/sin¢+cos¢/sin¢=k

=)(1+cos¢/sin¢)^2=(k)^2___squaring on both side .

we,get,..

=)1^2+cos^¢+2cos¢/sin^2¢2¢=k^2

=)1+cos^2+2cos¢=k^2sin^2¢

=)1+cos^2¢+2cos¢=k^2(1-cos^2¢)

=)(1+cos¢^2+2cos¢=k^2(1-cos^2¢)

=)1+cos¢^2¢+k^2cos^2¢+2cos¢=k^2

=)(1+k^2)cos^2¢+2cos¢+1=k^2

=)by using quadratic formula ..
roots,

=)-2-+√2^2-4*(1+k^2)*1=k^2

=)-2+-√4-4+4k^2=k^2

=)-2+-√4k^2=k^2

=)-2+-2k=k^2

=)k^+2k+2

and k^2-2k+2.

hope it help you

@rajukmar ☺