Question

(tan A + cot A + sec A )(tan A cot A - sec A ) =cosec ² A

Answer 1

Answer:

Step-by-step explanation:

LHS

= (tan A + cot A + sec A) (tan A + cot A - sec A)

Considering ( tan A + cot A) = x and sec A = y we can see the equation is in the form

(x + y ) (x - y)

which is equals to x² - y², applying the same

= (tan A + cot A)² - sec²A

Expanding bracket using (a +b)² = a² + 2ab + b²

= tan²A + 2.tan A. cot A + cot²A - sec²A

[∵ tan²Ф = sec²Ф - 1;    cot²Ф = cosec²Ф - 1 and tanФ.cotФ = 1]

we get

= (sec²A - 1) + 2 + (cosec²A - 1) - sec²A

= sec²A - 1 + 2 + cosec²A - 1 - sec²A

= cosec²A = RHS