Hello,
I am doin Trgiomominc Identites but I am having a bit of trouble with this one. Please help.
Express (1-tan^2 u)/(1+tan^2 u) in terms of Cos.
Possible answers.
a. 1/cos^2 u+1
b. 1/2cos^2 u+1
c. 1/cos^2 u -1
d. 1/2cos^2 u-1
PS. The [u] is that litte trig sumbol that looks like a [0] with a line through it.
Thanks
I am doin Trgiomominc Identites but I am having a bit of trouble with this one. Please help.
Express (1-tan^2 u)/(1+tan^2 u) in terms of Cos.
Possible answers.
a. 1/cos^2 u+1
b. 1/2cos^2 u+1
c. 1/cos^2 u -1
d. 1/2cos^2 u-1
PS. The [u] is that litte trig sumbol that looks like a [0] with a line through it.
Thanks
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... ( 1 - tan² Φ ) / ( 1 + tan² Φ )
= [ 1 - ( sin² Φ / cos² Φ ) ] / [ 1 + ( sin² Φ / cos² Φ ) ]
= ( cos² Φ - sin² Φ ) / ( cos² Φ + sin² Φ )
= [ cos² Φ - ( 1 - cos² Φ ) ] / (1)
= 2 cos² Φ - 1 ........................................… Ans.
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Hence, the correct option will be (d)
without that ' 1/ ' in the beginning.
_____________________________
Happy To Help !
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= [ 1 - ( sin² Φ / cos² Φ ) ] / [ 1 + ( sin² Φ / cos² Φ ) ]
= ( cos² Φ - sin² Φ ) / ( cos² Φ + sin² Φ )
= [ cos² Φ - ( 1 - cos² Φ ) ] / (1)
= 2 cos² Φ - 1 ........................................… Ans.
_____________________________
Hence, the correct option will be (d)
without that ' 1/ ' in the beginning.
_____________________________
Happy To Help !
_____________________________
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You are Welcome, Bruce !
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1+tan^2 u=1+sin^2u/cos^2u= (cos^2u+sin^2u) /cos^2u=1/cos^2u 1-tan ^2u = 1-sin^2u/cos^2u
=(cos^2u-sin^2u)/cos^u
so the problem be comes (cos^2u - sin^2u)= cos^2u-(1-cos^2u)
=2cos^2u -1
=(cos^2u-sin^2u)/cos^u
so the problem be comes (cos^2u - sin^2u)= cos^2u-(1-cos^2u)
=2cos^2u -1