Questions on Algebra: Trigonometry answered by real tutors!

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Question 150174: Please help me solve this problem!
If we establish an identity, -sin A csc A - sin^2 A - cos^2 A - tan A cot A would equal which of the following:
1. -2 + 2 sin^2 A
2. -3
3. 3 cos^2 A - 1
4. 3 cos^2 A - 2 sin^2 A
Thank you, Lennie: Please help me solve this problem!
If we establish an identity, -sin A csc A - sin^2 A - cos^2 A - tan A cot A would equal which of the following:
1. -2 + 2 sin^2 A
2. -3
3. 3 cos^2 A - 1
4. 3 cos^2 A - 2 sin^2 A
Thank you, Lennie
Answer by jojo14344(832) About Me  (Show Source):
You can put this solution on YOUR website!
-sin A csc A - sin^2 A - cos^2 A - tan A cot A ---------> eqn 1
Okay let's isolate section by section:
1st part: -sinAcscA
By reciprocal identities:
sinA=1/cscA----------> 1=sinAcscA, substitute in eqn 1 and looks:
=-1-sin^2A-cos^2A-tanAcotA
2nd part:
-sin^2A-cos^2A
By Pyth. identities:
sin^2 A + cos^2 A=1, since it has (-) on the 2nd part, then it will be = -1
.
Eqn 1 becomes now,
-1-1- tanA cotA
By reciprocal identities: tanA=1/cotA ----> 1=tanAcotA, substituting
= -1-1-1
= -3 --------------------> FINAL ANSWER no.2
Thank you,
Jojo