Question #3ff7f

1 Answer
Narad T.
Jan 23, 2018

See the proof below

Explanation:

We need

#tanA=sinA/cosA#

#cotA=cosA/sinA#

#cos^2A+sin^2A=1#

Therefore,

#"LHS"=tan^2A/(1+tan^2A)+cot^2A/(1+cot^2A)#

#=(sin^2A/cos^2A)/(1+sin^2A/cos^2A)+(cos^2A/sin^2A)/(1+cos^2A/sin^2A)#

#=sin^2A/(sin^2A+cos^2A)+cos^2A/(sin^2A+cos^2A)#

#=sin^2A+cos^2A#

#=1#

#="RHS"#

#"QED"#

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