Question

Show that sec^2 x + cosec^ x is greater than equal to
4.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

We know,

• sec²x = 1 + tan² x
• cosec²x = 1 + cot²x

So according to question,

sec²x + cosec²x = 2 + tan²x + cot²x

But ,

We know that A.M > G.M

So ,

(tan²x + cot²x)/2  >  √(tan²x.cot²x)

⇒ tan²x + cot²x  >  2 × 1

⇒ tan²x + cot²x  >  2

Now ,

Adding 2 on both sides ,

(1 + tan²x) + (1 + cot²x)  >  2 + 2

⇒ sec²x + cosec²x  >  4

Hence proved !!!!!