Question

prove that : (cosec2A‒ 1)(sec A+ 1)(sec A‒ 1) = 1

Answer 1

$\huge\underline\mathbb{\red S\pink {O}\purple {L} \blue {UT} \orange {I}\green {ON :}}$

On LHS

By identity (a+b)(a-b) = a² - b²

we get

(cosec²A -1)(sec²A-1)

Now by identity (1 + tan²A = sec²A and 1 + cot²A = cosec²A)

Cot²A × tan²A

Now as cotA = 1/tanA

1/tan²A. × tan²A

=1

LHS=RHS

hence proved

Answer 2

Answer:

Hey mate here is your answer

Step-by-step explanation:

Oh LHS

By identity (a+b)(a-b) =a²-b²

we get

(cosec²A-1)(sec²A-1)

Now by identify (1+tan²A=sec²Aand 1 +cot2A =cosec²A)

cot2A* tan²A

Now as cotA=1/tanA

1/tan²A*tan²A=1

LHS=RHS

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