Need help in this trigo identities question!

[deedre]

The question asks to prove that:

tan^2(x) + cot^2(x) +2 = cosec^2(x)sec^2(x)

Help would be greatly appreciated and thanks for the trouble!

 

[Deleted member 4993]

The question asks to prove that:

tan^2(x) + cot^2(x) +2 = cosec^2(x)sec^2(x)

Help would be greatly appreciated and thanks for the trouble!

use tan^2(x) +1 = sec^2(x) and cot^2(x) +1 = cosec^2(x) and sin^2(x) + cos^2(x) = 1

What are your thoughts?

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[stapel]

The question asks to prove that:

tan^2(x) + cot^2(x) +2 = cosec^2(x)sec^2(x)

Help would be greatly appreciated and thanks for the trouble!

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

For instance, you first converted everything on the right-hand side to sines and cosines. You noted the simple form you obtained as a result. Then you converting the left-hand side to sines and cosines. You converted all three terms to a common denominator, and then noted that the numerator was the square of a (trig) binomial, which easily simplifies. And... then what?

Please be complete. Thank you!

 

[Ishuda]

The question asks to prove that:

tan^2(x) + cot^2(x) +2 = cosec^2(x)sec^2(x)

Help would be greatly appreciated and thanks for the trouble!

You might have better luck proving
tan^2(x) + cot^2(x) +2 = cosec^2(x) + sec^2(x)

 

[Deleted member 4993]

You might have better luck proving
tan^2(x) + cot^2(x) +2 = cosec^2(x) + sec^2(x)

cosec^2(x) + sec^2(x) = cosec^2(x) * sec^2(x)

 

[Ishuda]

cosec^2(x) + sec^2(x) = cosec^2(x) * sec^2(x)

Sorry, should have been more clear. Yes, but as an intermediate step, one is easier than the other to prove. IMO, at least.