19 -1,2 both portion pls very fast

19 .   Evaluate   :   cosec 2 63 ° + tan 2 24 ° cot 2 66 ° + sec 2 27 ° + sin 2 63 ° + cos 63 °   sin 27 °   + sin 27 ° sec 63 ° 2 cosec 2 65 ° - tan 2 25 ° OR If   sinθ + cosθ = 2 ,   then   evaluate :   tanθ + cotθ

Dear Student,

Answer(i):

=cosec263+tan224cot266+sec227+sin263+cos63sin27+sin27sec632cosec265-tan225=cosec290-27+tan224cot2(90-24)+sec227+sin2(90-27)+cos(90-27)sin27+sin27sec(90-27)2cosec2(90-25)-tan225=sec227+tan224tan224+sec227+cos227+sin27 sin27+sin27cosec272sec225-tan225=1+cos227+sin227+sin27 1sin272=1+1+12=1+1=2

Answer(ii)


Since,sin θ +cos θ=2squaring both the sides we get,sin θ +cos θ2=22sin2 θ+cos2 θ+2sin θ cos θ=2or, 1+2sin θ cos θ=2or, 2sin θ cos θ=1or, sin θ cos θ=12.....(i)Now, =tan θ+cot θ=sin θcos θ+cos θsin θ=sin2 θ+cos2 θsin θ cos θ=1sin θ cos θ=112      from (i), as sin θ cos θ=12=2


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