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Trigonometry: Trigonometric Identity-Examples
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Trigonometric Identity: Examples

Example: Prove the following identity:
(1 - cos)/(1 + cos) = (cosec - cot)2
Solution: Given,
L.H.S.
(1 - cos)/(1 + cos)
= (1 - cos)/(1 + cos) x (1 - cos)/(1 - cos)
= (1 - cos)2/(1 - cos2)
= [(1 - cos)/sin]2...........(As 1 - cos2 = sin2)
= [1/sin - cos/sin]2
= (cosec - cot)2
R.H.S.

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Example: Prove 
(cosec - sin)(sec - cos)(tan + cot) = 1
Solution:
L.H.S.
(cosec - sin)(sec - cos)(tan + cot)
= (1/sin - sin)(1/cos - cos)(sin/cos + cos/sin)
= [(1 - sin2)/sin][(1 - cos2)/cos][(sin2 + cos2)/sincos]
= cos2/sin x sin2/cos x 1/sincos
= sin2cos2/sin2cos2
= 1
R.H.S.

 
   
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