Cotθ-cosecθ=p. Then Cotθ+cosecθ=?

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Answer 1 · 2018-03-22T15:53:03

The answer is #cottheta + csctheta = -1/p#

We have

#cottheta - csctheta = p#

#costheta/sintheta - 1/sintheta = p#

#(costheta - 1)/sintheta = p#

Now let #cottheta + csctheta = A#.

#(costheta + 1)/sintheta= A#

Multiplying the first equation with the second, we get

#((costheta - 1)/sintheta)(costheta + 1)/sintheta = pA#

#(cos^2theta -1)/sin^2theta = pA#

#-sin^2theta/sin^2theta = pA#

#-1 = pA#

Thus

#A = -1/p#

Therefore, #cottheta + csctheta = -1/p#.

Hopefully this helps!

Answer 2 · 2018-03-22T15:59:27

#cottheta+cosectheta=-1/p#

We have ,

#cottheta-cosectheta=p.#

#=>color(blue)(cosectheta-cottheta=-p.......to#(1)

We know that

#color(red)(cosec^2theta-cot^2theta=1#

#=>color(blue)((cosectheta-cottheta))(cosectheta+cottheta)=1#

#=>color(blue)((-p))(cosectheta+cottheta)=1#,...from (1)

#=>cosectheta+cottheta=1/(-p)#

#i.e. cottheta+cosectheta=-1/p#