Question

(cosec A – sin A)(sec A – cos A

Answer 1

Answer:

Step-by-step explanation:

We have to just simplify both side of the question.

Now, taking L. H. S =

(cosecA - sinA)×(secA - cosA)

= (1/sinA - sinA)×(1/cosA - cosA)

= (1-sin²A)/sinA × (1-cos²A)/cosA

= cos²A/sinA × sin²A/cosA

= cos²Asin²A/cosAsinA

= cosAsinA

Now, R. H. S =

1/(tanA + cotA)

= 1/(sinA/cosA + cosA/sinA)

= 1/[(sin²A + cos²A)/cosAsinA]

= 1/[(1/cosAsinA)]

= cosAsinA

Since L. H. S. = R. H. S.

Therefore the given equation is proof.

Answer 2

Answer:

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

Step-by-step explanation:

cosec A= $\frac{1}{sin A}$

$\frac{1}{sin A} - sin A$

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

[$sin^{2} A + cos^{2} A = 1$

$1 - sin^{2} A = cos^{2} A$]

Substitute: $\frac{cos^{2} A}{sin A}$ -----(1)

sec A=$\frac{1}{cos A}$

$\frac{1}{cos A} - cos A$

$\frac{1-cos^{2} A }{cos A}$

[$sin^{2} A + cos^{2} A = 1$

$1 - cos^{2} A = sin^{2} A$]

Substitute: $\frac{sin^{2} A }{cos A}$ -----(2)

(1)x(2)

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