1.

If cosectheta=t+1/4t(t not included in fraction), then prove that cosectheta + cottheta = 2t or 1/2t

Answer»

√{(sec β -1)/(secβ +1)}

= √{(1 - cosβ)/(1+cosβ)} (by dividing every term by secβ

= √{(1-cosβ)²/(1-cos²β)} ( by multiplying numerator & denominator by (1-cosβ)

= √{(1- cosβ)² / sin²β }

= (1-cosβ) / sinβ …………………. (1)

Similarly, √{(secβ +1)/(secβ -1)

= √{(1+cosβ) / (1-cosβ) } ( as done above)

= √{(1+cosβ)² / (1-cos²β) }

= √{(1+cosβ)² / sin² β }

= (1+cosβ ) / sinβ ……………. (2)

By adding (1) & (2)

LHS =

= { 1-cosβ + 1+cosβ } / sinβ

= 2/sinβ

= 2 cosec β

= RHS

[ Hence PROVED]


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