Find the principal and general solutions of the following equations:(i) tanx=√3 (ii) secx=2(iii) cotx=−√3(iv) cosecx=−2
(i) tanx=√3=tanπ3=tan4π3
Hence principal solution of tanx=√3
are π3 and 4π3
tanx=√3=tanπ3
Hence general solution is given by,
x=nπ+π3 where n∈Z
(ii) secx=2=secπ3=sec5π3
Hence principal solution of secx=2
are π3 and 5π3
secx=2=secπ3
Hence general solution is given by,
x=2nπ±π3, where n∈Z
(iii)cotx=−√3=cot5π6=cot11π6
Hence principal value of cotx=−√3
are 5π6 and 11π6
cotx=−√3=cot5π6
Hence general solution is given by,
x=nπ+5π6, where n∈Z
(iv) cscx=−2=csc7π6=csc11π6
Hence principal solution of cscx=−2
are 7π6 and 11π6
cscx=−2=csc7π6
Hence general solution is given by,
x=nπ+(−1)n7π6, where n∈Z