CBSE Class 11-science Answered
Solve for x
3tanx + cotx = 5cosecx
Asked by dssinghania1234 | 27 Oct, 2018, 10:20: AM
![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](https://images.topperlearning.com/topper/tinymce/cache/ec88a9c667f01fb6bc2b999564891758.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/48dfa1ebe3f4d4a270e6f92b20df6f23.png)
Answered by Ram Singh | 28 Oct, 2018, 16:05: PM
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