Question

tan²∅+cot²∅+2=sec²∅×cosec²∅

Answer 1

Step-by-step explanation:

tan²A + cot²A + 2 = sec²A x cosec²A

L.H.S

tan²A + cot²A + 2

= sin²A/cos²A + cos²A/sin²A + 2

= sin⁴A + cos⁴A + 2sin²A.cos²A/sin²A.cos²A

= (sin²A + cos²A)²/sin²A.cos²A

= (1)²/sin²A.cos²A

= 1/sin²A.cos²A (1)

R.H.S

sec²A x cosec²A

= 1/cos²A x 1/sin²A

= 1/sin²A.cos²A (2)

From (1) and (2),

L.H.S = R.H.S is proved.

Note : (Instead of ∅ I used A)