SOLUTION: Please use identities and the complimentary angles to find the exact value of: 1 + tan^2 5(degrees)

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Question 527043: Please use identities and the complimentary angles to find the exact value of:
1 + tan^2 5(degrees) - csc^2 85(degrees)
Thank You very much
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
Please use identities and the complimentary angles to find the exact value of:
1 + tan^2 5(degrees) - csc^2 85(degrees) .
**
1+tan^2(5�)-csc^2(85�)
1+(sin^2(5�))/(cos^2(5�))-1/(sin^2(85�)
Identity: sin(90�-x)=cosx
csc^2(85�)=1/sin^2(85�)
sin^2(85�)=sin^2(90�-5�)=cos^2(5�)
..
1+(sin^2(5�))/(cos^2(5�))-1/(sin^2(85�)
1+[(sin^2(5�))/(cos^2(5�))]-1/(cos^2(5�)
LCD:cos^2(5�)
[cos^2(5�)+sin^2(5�)-1]/(cos^2(5�))
Identity: cos^2(x)+sin^2(x)=1
(1-1)/cos^2(5�)=0/cos^2(5�)=0
ans:
Exact value of given function=0

SOLUTION: Please use identities and the complimentary angles to find the exact value of: 1 + tan^2 5(degrees) - csc^2 85(degrees) Thank You very much