tan 0 - 001015. Prove that ————— = tan? 0 - cot? 0.sin B cos

1.	tan 0 - 001015. Prove that ————— = tan? 0 - cot? 0.sin B cos O
Answer» ( 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. Hit like if you find it useful

tan 0 - 001015. Prove that ————— = tan? 0 - cot? 0.sin B cos O

Answer»

( 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.

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