Question

cot²A ( Sec A-l )/(1+sinA) + sec ²A (sinA-1)/1+secA)=0​

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sayajiraogaikw

sayajiraogaikw

08.10.2017

Math

Secondary School

+5 pts

Answered

Prove that cot2A(secA-1/1+sinA) + sec2A(sinA-1/1+secA) = 0

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sachinkumar121

sachinkumar121 Ambitious

cot²A(secA-1/1+sinA)+sec²A(sinA-1/1+secA)=0

L.H.S.

cot²A(secA-1/1+sinA)+sec²A(sinA-1/1+secA)

=cot²A[(secA-1)(1-sinA)/(1+sinA)(1-sinA)]+sec²A[(sinA-1)(secA-1)/(secA+1)(secA-1)]

=cot²A[(secA-secA.sinA-1+sinA)/(1-sin²A)]+sec²A[(sinA.secA-sinA-secA+1)/(sec²A-1)]

=cot²A[(secA-secA.sinA-1+sinA)/cos²A]+sec²A[(sinA.secA-sinA-secA+1)/tan²A]

=(cos²A/sin²A)[(secA-secA.sinA-1+sinA)/cos²A]+[sec²A(sinA.secA-sinA-secA+1)](cos²A/sin²A)

=[(secA-secA.sinA-1+sinA)/sin²A]+[(sinA.secA-sinA-secA+1)/sin²A]

=(secA-secA.sinA-1+sinA+sinA.secA-sinA-secA+1)/sin²A

=0/sin²A

=0

R.H.S=L.H.S

Hence proved…