Question

cosec A (1+ cos A)(cosec A - cot A) = 1​

Answer 1

How to prove that cosec A(1+cos A)(cosec A-cot A)=1

step-by-step Explanation:

take L.H.S :

=>cosec A(1+cos A)(cosec A-cot A)      

=> 1/sinA(1+cosA)(1/sinA-cosA/sinA)        [we know that cosec A = 1/sin A]

=>(1+cosA)/sinA * (1-cosA)/sinA              [we know that cot A = cos A/sinA]

=>(1+cosA)(1-cosA)/sin^2 A    [1/sinA-cosA/sinA = 1-cosA/sinA (like fraction)]

=>1-cos^2 A / sin^2 A             [1^2=1*1=1]  [we know that (p-q)(p+q)=p^2-q^2]

=>sin^2 A/sin^2 A  [from identity,sin^2 A+cos^2 A=1 => sin^2 A = 1-cos^2 A]

=>1

=>R.H.S

HENCE PROVED