Question

Tan^2o & cot²0 +2=Sec^2o cosec²o​

Answer 1

★____question:

• Prove that tan²∅ + cot²∅= sec²∅cosec²∅

★____Solution:

As we know,

• tan∅ = sin∅/cos∅ ......(1)
• cot ∅= cos∅/sin ∅.....(2)

Now let's lake LHS

→ tan²∅+ cot²∅ +2

→ sin²∅/cos²∅ + cos²∅/sin²∅+2

→ sin⁴∅+cos⁴∅/cos²∅sin²∅ +2

→ sin⁴∅+cos⁴∅+2cos²∅sin²∅/cos²∅sin²∅

→(sin²∅+cos²∅)²/cos²∅sin²∅

• As sin²∅+cos²∅= 1

→1/cos²∅sin²∅

• as 1/sec∅= cos∅
• 1/sin∅= cosec∅

→ cos²∅cosec²∅ which is RHS

$\rule{200}2$