Question

If A is acute angle then prove that
1+cot^2A = cosec^2A
Pls answer fast

Answer 1

Step-by-step explanation:

Taking LHS

1 + cot^2A

{cotA = cosA/sinA}

1 + cos^2A/sin^2A

(sin^2A + cos^2A)/ sin^2A

we know that

sin^2A + cos^2A = 1

1/sin^2A

{cosecA = 1/sinA}

1/sin^2A = cosec^2A

hence proved

Answer 2

Answer with Step-by-step explanation:

A is acute angle

Proof:

LHS

$1+cot^2A$

We know that

$cotA=\frac{cosA}{sinA}$

Substitute the value then we get

$1+\frac{cos^2A}{sin^2A}$

$\frac{sin^2A+cos^2A}{sin^2A}$

$\frac{1}{sin^2A}$

Using identity :$sin^2A+cos^2A=1$

$cosec^2A$

Using formula $cosecA=\frac{1}{sinA}$

LHS=RHS

Hence, proved.

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