Question

prove that
Cot theta + Tan phi/ tan theta + Cot phi = tan theta * cot phi

Answer 1

Answer:

refers to the above photo

Answer 2

Given :   (cotθ + tanΦ )/(tanθ + cotΦ) = tanθCotΦ

To Find : Prove that

Solution:

(cotθ + tanΦ )/(tanθ + cotΦ) = tanθCotΦ

LHS =  (cotθ + tanΦ )/(tanθ + cotΦ)

cotx = 1/tanx  , tanx = 1/cotx

=   (cotθ + tanΦ )/(1/cotθ + 1/tanΦ)

= (cotθ + tanΦ )/((tanΦ+cotθ )/(cotθtanΦ))

= (cotθ + tanΦ )/((cotθ+tanΦ )/(cotθtanΦ))

= 1/ (1  / (cotθtanΦ))

 1/(1/x)  = x

= cotθtanΦ

= RHS

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