Trignometry

Asked by aishwarya1 | 22nd Dec, 2009, 07:06: PM

Expert Answer:

(tanθ + sinθ)/(tanθ - sinθ) = [(sinθ + cosθsinθ)/cosθ]/[(sinθ - cosθsinθ)/cosθ] 

= [sinθ(1 + cosθ)]/[sinθ(1 - cosθ)]

= (1 + cosθ)/(1 - cosθ)

= (1 + 1/secθ)/(1 - 1/secθ)

= (secθ + 1)/(secθ - 1)

Multiply and divide by (secθ - 1)

= (secθ + 1)(secθ - 1)/(secθ - 1)2

= (sec2θ - 1)/(secθ - 1)2

= tan2θ/(secθ - 1)2 ...........using the identity 1 + tan2θ = sec2θ

Regards,

Team,

TopperLearning. 

 

Answered by  | 22nd Dec, 2009, 09:16: PM

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