CBSE Class 11-science Answered
Prove the following trigonometric identity
Asked by | 16 Apr, 2010, 07:08: PM
Expert Answer
cosecx - sinx = a3
1/sinx - sinx = a3
(1 - sin2x)/sinx = a3
cos2x/sinx = a3
(cos2x/sinx)2/3 = a2
Similarly,
(sin2x/cosx)2/3 = b2
Now, a2b2(a2+b2) =
[(cos2x/sinx)(sin2x/cosx)]2/3{(cos2x/sinx)2/3 + (sin2x/cosx)2/3} =
[cosx sinx]2/3{[(cos3x)2/3 + (sin3x)2/3 ]/(sinxcosx)2/3} =
[cosx sinx]2/3{[cos2x + sin2x ]/(sinxcosx)2/3} =
[cosx sinx]2/3{1/(sinxcosx)2/3} = 1.
Regards,
Team,
TopperLearning.
Answered by | 16 Apr, 2010, 08:58: PM
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