prove tandeter/1-cotdeter+cotdeter/1-tandeter=1+tandeter+cotdeter
prove tandeter/1-cotdeter+cotdeter/1-tandeter=1+tandeter+cotdeter
Jacob , 7 Years ago
Grade 11
Trigonometry> prove tandeter/1-cotdeter+cotdeter/1-tand...
1 Answers
Arun
Dear student
LHS=tanx1−cotx+cotx1−tanx
=tan2xtanx(1−cotx)+cotx1−tanx
=cotx1−tanx+tan2xtanx−tanxcotx
=cotx1−tanx−tan2x1−tanx
=1tanx−tan2x1−tanx
=1−tan3xtanx(1−tanx)
=(1−tanx)(1+tanx+tan2x)tanx(1−tanx)
=tanx+sec2xtanx
=tanxtanx+sec2xtanx
=1+secx⋅secx⋅(cosxsinx)
=1+secx⋅(1sinx)
=1+secx⋅cscx
=1 + 1 / sinx. cosx
=1 + sin^2x + cos^2x / sinx cosx
= 1 + tanx + cotx
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