Question

(sec^2a-1) (cosec^2a-1)​

Answer 1

Answer:

1

Step-by-step explanation:

since sec theta= 1/ cos theta and cosec theta = 1/ sin theta

So, the given expression becomes

$=(\frac{1}{cos^2a} -1)(\frac{1}{sin^2a} -1)\\=(\frac{1- cos ^2a}{cos^2a} )(\frac{1- sin ^2a}{sin^2a} )$expression 2

Since we know by trignometric identity,

$=1- cos^2a= sin^2a\\=1-sin ^2a= cos^2a$

Substituting value of 1- cos^2a and 1-sin^2a in expression 2

$=(\frac{sin^2a}{cos^2a})( \frac{cos^2a}{sin^2a} )$

after cancellation

=  1