Prove that (cosec A-cot A)(cosec A-cotA)=(1-cos A)/(1+cos A)

Asked by Aditya Chakravarty | 22nd May, 2013, 12:30: PM

Expert Answer:

(cosec A-cot A)(cosec A-cotA)
= (1/sinA - cosA/sinA) (1/sinA - cosA/sinA)
= (1-cosA)^2 /(sinA)^2
= (1-cosA)^2 /(1-(cosA)^2) 
= (1-cosA)^2 /(1-(cosA)) (1+cosA)  (Using a^2 - b^2 = (a-b)(a+b))
= (1-cosA)/(1+cosA) = RHS 
Hence proved

Answered by  | 23rd May, 2013, 02:59: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.