Question #6a3fa

2 Answers
P dilip_k
Nov 28, 2017

#3cot^2theta+10cscθ=5#

#=>3cos^2theta/sin^2theta+10/sinθ=5#

#=>3cos^2theta+10sintheta=5sin^2theta#

#=>3-3sin^2theta+10sintheta=5sin^2theta#

#=>8sin^2theta-10sintheta-3=0#

#=>8sin^2theta-12sintheta+2sintheta-3=0#

#=>4sintheta(2sintheta-3)+1(2sintheta-3)=0#

#=>(2sintheta-3)(4sintheta+1)=0#

#=>(2sintheta-3)=0 and(4sintheta+1)=0#

#(2sintheta-3)# Not possible

When

#4sintheta+1=0#

#=>sintheta=-1/4=sin165.5^@#

#=>theta=165.5^@#

Nghi N
Nov 29, 2017

#194^@48 ; 345^@52# for (0, 360)

Explanation:

#3cot^2 t + 10csc t = 5#
After development and simplification, we get
#f(x) = (2sin t - 3)(4sin t + 1) = 0#
Either factor should be zero.
a. 2sin t - 2 = 0 --> #sin t = 3/2#. Rejected because > 1
b. 4sint + 1 = 0 --> 4sin t = 1
#sin t = - 1/4#
Calculator and unit circle give 2 solutions:
#t = - 14^@ 48, or t = 360 - 14.48 = 345^@52# (co-terminal)
#t = 180 + 14.48 = 194^@48#

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