Question

(cosec A - sin A) (sec A - cos A) (tan A + cot A) = 1​

Answer 1

Step-by-step explanation:

=(

sinA

1

−sinA)(

cosA

1

−cosA)(

cosA

sinA

+

sinA

cosA

)

= (\dfrac{1-sin^{2}A}{sinA})(\dfrac{1-cos^{2}A}{cosA})(\dfrac{sin^{2}A + cos^{2}A}{sinA\:cosA}=(

sinA

1−sin

2

A

)(

cosA

1−cos

2

A

)(

sinAcosA

sin

2

A+cos

2

A

= (\dfrac{cos^{2}A}{sinA})(\dfrac{sin^{2}A}{cosA})(\dfrac{1}{sinA\:cosA})=(

sinA

cos

2

A

)(

cosA

sin

2

A

)(

sinAcosA

1

)

= \dfrac{cosA \: sinA}{sinA \: cosA} = 1=

sinAcosA

cosAsinA

=1