Question

cos theta minus sin theta + 1 upon cos theta + sin theta minus 1 equal to cosec theta + cot theta

Answer 1

$<h4>REFER THE ATTACHMENT. <h4>$

Answer 2

Proper Question:

Cosθ - Sinθ +1 ÷ Cosθ + Sinθ - 1 = Cosecθ + Cot θ



Step By Step Explanation:


Cosθ - Sinθ +1 ÷ Cosθ + Sinθ - 1 = Cosecθ + Cot θ


✏ Cosθ - Sinθ +1 ÷ Cosθ + Sinθ - 1

✏ Cosθ/Sinθ - Sinθ/Sinθ + 1 /Sinθ ÷ Cosθ/Sinθ + Sinθ/Sinθ - 1/Sinθ

✏ Cotθ - 1 + Cosecθ ÷ Cotθ + 1 - Cosecθ

✏ Cotθ+Cosecθ - 1 ÷ Cotθ - Cosecθ + 1

✏ Cotθ + Cosecθ - (Cosec²θ - Cot²θ) ÷ Cotθ - Cosecθ + 1

✏ (Cotθ + Cosecθ) [ 1 -(Cotθ - Cosecθ)] ÷ Cot θ - Cosecθ + 1

✏ (Cotθ + Cosecθ) (Cotθ - Cosecθ +1) ÷ Cotθ - Cosecθ +1

✏ Cancelled {Cotθ - Cosecθ +1} on upper and lower Side!

✏ Cot θ + Cosec θ

✒ Cosec θ + Cot θ

It's Proved!