Question

prove that (1 + cot A + tan A)*(sin A - cos A) = sec A/cosec^2 A - cosec A / sec ^2 A​

Answer 1

L.H.S

=(1+ cos A /sinA + sinA/cosA)(sinA-CosA

=(cosAsinA + cos^2A + Sin^2A/cosAsinA )(sinA- cosA). .....(take LCM)

=(cosA sinA + 1/cosAsinA) (sin A- cos A ). .....(sin^2A +cos^2 A = 1)

= cosA sin^2A -cos^2 A sin A + sinA - cosA / cos A sin A

=sinA ( 1 - cos^2 A) -cosA (1- sin^2A)/ cosAsinA

sinA sin^2A - cos A cos^2 /cosAsinA

sin^3A - cos^3A/cosAsinA

sin^3A/ sinAcosA - cos^3A/cosA sinA

sin^2A /cosA - cos^2 /sinA

=secA/ cosecA - cosecA / sec^2. HENCE PROVED

L.H.S = R.H.S

Answer 2

I hope so you like my answer