Question

TanA-CotA/SinA.cosA=Sec^2A-Cosec^2A=Tan^2A-Cot^2A

Answer 1

Hi ,

( tanA - cotA )/( sinAcosA )

= [(sinA/cosA)-(cosA/sinA)]/(sinAcosA)

= ( sin²A - cos² A )/ sin²Acos²A

= ( sin² A/sin²Acos²A)-(cos²A/sin²Acos²A )

= ( 1/cos² A ) - ( 1/sin² A )

= sec² A - cosec² A ----( 1 )

= ( 1 + tan² A ) - ( 1 + cot² A )

= 1 + tan² A - 1 - cot² A

= tan² A - cot² A

Hence proved.

: )

Answer 2

Hi,

Please see the attached file!


Thanks