Question

plz solve this frnds, class 10 trigonometry.

Answer 1

Trigonometry,

First of all, let 'e' insted of theta,

We have,
$\frac{tane - cote}{sine \times cose}$

Have to prove that this = tan²e - cot²e

Solution,
$\frac{tane - cote}{sine \times cose}$

{(sine/cose) - (cose/sine)}/sine.cose

= {(sin²e - cos²e)/sine.cose}/sine.cose

= (sin²e - cos²e)/sin²e.cos²e

= (sin²e)/sin²e.cos²e - (cos²e)/sin²e.cos²e

= 1/cos²e - 1/sin²e

= sec²e - cosec²e

= 1 + tan²e - 1 - cot²e

= tan²e - cot²e [proved]