Question

(cosec A-sin A) (sec A -cos A) (tan A + cot A)​

Answer 1

Answer:

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Answer 2

Given :The trigonometric expression is ...

$(cosecA-sinA)(secA-cosA)(tanA+cotA)$

To find : the numerical value of given trigonometric expression.

solution :

$(cosecA-sinA)(secA-cosA)(tanA+cotA)$

$=\left(\frac{1}{sinA}-sinA\right)\times\left(\frac{1}{cosA}-cosA\right)\times\left(\frac{sinA}{cosA}+\frac{cosA}{sinA}\right)$

$=\left(\frac{1-sin^2A}{sinA}\right)\times\left(\frac{1-cos^2A}{cosA}\right)\times\frac{sin^2A+cos^2A}{sinAcosA}$

we know, sin²x + cos²x = 1

so, 1 - sin²A = cos²A

1 - cos²A = sin²A

and sin²A + cos²A = 1

$=\left(\frac{cos^2A}{sinA}\right)\times\left(\frac{sin^2A}{cosA}\right)\times\left(\frac{1}{sinAcosA}\right)$

$=\frac{cos^2Asin^2A}{sinAcosA}\frac{1}{sinAcosA}$

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

Therefore the value of $(cosecA-sinA)(secA-cosA)(tanA+cotA)$ is 1.