Question

prove that tanA-cotA/sinA*cosA=tan^2A-cot^2A​

Answer 1

Answer:

RHS = tan²A - cot²A

=  ( tan A - cotA) (tanA + cotA) {(a-b) (a + b) = a² - b²}

we know that ,

tan A = sinA/cosA

cot A = cosA/sinA

= (tanA - cotA) (sinA/cosA + cosA/sinA)

(sinA/cosA + cosA/sinA) :- LCM = sinA cosA

= (tanA - cotA) ( sin²A + cos²A/sinA cosA)

but , we know that , sin²A + cos²A = 1

so,

=  (tanA - cotA) ( 1/sinAcosA)

= (tanA - cotA)/sinAcosA

= LHS

HENCE PROVED

Step-by-step explanation:

Answer 2

Step-by-step explanation:

above pic will help u