Solve for x 

3tanx + cotx = 5cosecx

 

Asked by dssinghania1234 | 27th Oct, 2018, 10:20: AM

Expert Answer:

3 space tan x plus c o t space x equals 5 cos e c space x
3 fraction numerator sin x over denominator cos x end fraction plus space fraction numerator cos space x over denominator sin space x end fraction equals fraction numerator 5 over denominator sin space x end fraction
fraction numerator
3 space sin squared x plus cos squared x over denominator cos space x space sin space x end fraction equals fraction numerator 5 over denominator sin space x end fraction

fraction numerator
2 space sin squared x plus sin to the power of 2 space end exponent x plus cos squared x over denominator cos space x space sin space x end fraction equals fraction numerator 5 over denominator sin space x end fraction
fraction numerator
2 space sin squared x plus space 1 over denominator cos space x space sin space x end fraction equals fraction numerator 5 over denominator sin space x end fraction

2 sin cubed x space plus sin x equals 5 sin x space cos x
2 sin cubed x space plus sin x minus 5 sin x space cos x equals 0

sin x space left parenthesis 2 space sin squared x minus 5 cos x space plus 1 right parenthesis space equals 0
s o space sin x equals 0 space O R space space 2 space sin squared x minus 5 cos x space plus 1 equals 0
s o space x equals space n pi space space O R space space 2 space left parenthesis 1 minus cos squared x right parenthesis minus 5 space cos x space plus 1 equals 0
2 minus 2 cos squared x minus 5 space cos x space plus 1 equals 0
2 cos squared x plus 5 space cos x space minus 3 equals 0
2 cos squared space x plus space 6 space cos space x minus cos space x space minus 3 equals 0
2 cos x left parenthesis space cos x plus 3 right parenthesis minus 1 left parenthesis cos space x plus 3 right parenthesis space equals 0

left parenthesis 2 space cos x minus 1 right parenthesis left parenthesis cos space x plus 3 right parenthesis equals 0
cos space x equals 1 half space o r space cos space x space equals 3
sin c e space cos space x equals 3 space n o t space p o s s i b l e space space left parenthesis negative 1 less or equal than cos x less or equal than 1 right parenthesis

cos space x equals 1 half


cos x space equals space cos left parenthesis pi over 3 right parenthesis
h e n c e space x equals 2 n pi plus-or-minus pi over 3

h e n c d e space x equals n pi space o r space x equals 2 n pi plus-or-minus pi over 3
b u t space x equals n pi space e q u a t i o n space n o t space s a t i s f y space sin c e space c o t space x space i s space u n d e f i n e d space
s o space x equals 2 n pi plus-or-minus pi over 3

Answered by Ram Singh | 28th Oct, 2018, 04:05: PM