Question

prove it with trigonometric identities​

Answer 1

$\mathbb{\huge{SOLUTION:-}}$

Your question has a slight error

TO PROVE :

sec²Φ+ cosec²Φ = (tanΦ + cotΦ)²

PROOF:

LHS:

As we know,

sec²Φ = 1 + tan²Φ

cosec²Φ = 1 + cot²Φ

Hence, we get

sec²Φ + cosec²Φ

= 1 + tan²Φ + 1 + cot²Φ

= 2 + tan²Φ + cot²Φ

= (tanΦ + cotΦ)²

(We can write it like that because (tanΦ×cotΦ = 1) So while expanding

(tanΦ + cotΦ)² we get,

tan²Φ + 2 tanΦcotΦ + cot²Φ

= tan²Φ + cot²Φ + 2)