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Introduction to Trigonometry
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16/06/2021 11:46 am
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Evaluate:
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2A + cot2A
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16/06/2021 11:48 am
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2A + cot2A
L.H.S. = (sin A + cosec A)2 + (cos A + sec A)2
It is of the form (a+b)2, expand it
(a+b)2 = a2 + b2 + 2ab
= (sin2A + cosec2A + 2 sin A cosec A) + (cos2A + sec2A + 2 cos A sec A)
= (sin2A + cos2A) + 2 sin A(1/sin A) + 2 cos A(1/cos A) + 1 + tan2A + 1 + cot2A
= 1 + 2 + 2 + 2 + tan2A + cot2A
= 7+tan2A+cot2A = R.H.S.
Therefore, (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2A + cot2A
Hence proved.