Question

if cosecthete + costheta=k then prove that cos theta = ksquare -1/ksquare+1

Answer 1

cot tita + cosec tita = K  ------ 1

(cosec tita+ cot tita ) (cosec tita - cos tita) = 1 ( (a+b)(a-b) = a^2 + b^2 ) (cosec^2 - cot^2 = 1)

cosec tita - cos tita = 1 / k

cosec T + cot T = k
cosec T - cot T = 1/k

==>  cot T =  K^2 - 1 / k  -- 2

===> do the same but this time do coesec T = K^2 +1 /k

==> you know cot T = cos T / sin T  and cosec T = 1/ sin T

==>  cos T / 1 / k / K^2 + 1 = K^2 - 1 / k  form 2

==> cos T = K^2 - 1 / k / K^2 +1 / k (k k get cancels ) hence proved


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