A few days ago

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Prove that cosecA + cotA = 1/(cosecA-CotA) provings that A exists?

This has got me stumped has got me stumped, how can just changins the sign and putting it under 1 equal the same thing? i tried this ended up writing loads of stuff not knowing which direction to go in, and still not fuinding a solution.

Thank you to everyone who is willing to help me

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

when ever you want to prove a trig identity, you start with the most complicated side of the equality

first note

sin²a = 1 – cos²a

divide both sides of this by sin²a gives

1 = csc²a – cot²a………(*)

you probably learnt this rule in class

next to prove

cscA + cotA = 1/(cscA-cotA)

you need to use a very common trick in maths which is multiplying by 1 (in disguise)

in this case you multiply

1/(cscA-cotA) by

(cscA + cotA) / (cscA + cotA) which is 1 in disguise

proof

1/(cscA-cotA)

= 1/(cscA-cotA) * (cscA + cotA) / (cscA + cotA)

= (cscA + cotA) / (cscA – cotA)(cscA + cotA)

= (cscA + cotA) / (csc²A – cot²A)

= (cscA + cotA) / 1 …………. by (*)

= (cscA + cotA)

end proof

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Prove that cosecA + cotA = 1/(cosecA-CotA) provings that A exists?

Prove that cosecA + cotA = 1/(cosecA-CotA) provings that A exists?

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