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prove that sec A(1- sin A) (secA+ tan A) = 1
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Asked by pandeydivyanshu42 | 19 Jun, 2020, 12:52: PM
answered-by-expert Expert Answer
The trigonometric ratios which will be used in this question are: secA = 1/cosA, tanA = sinA/cosA
The identity used will be (a - b)(a + b) = (a2 - b2)
Taking the left hand side,
secA(1 - sinA)(secA + tanA)
= (1/cosA)(1 - sinA)(1/cosA + sinA/cosA)
= (1/cosA)(1 - sinA)(1+ sinA)/cosA
= (1/cosA)(1/cosA)(1 - sin2A)
= (1/cos2A)(cos2A)                      Since 1 - sin2A = cos2A
= 1
Hence, secA(1 - sinA)(secA + tanA) = 1
Answered by Renu Varma | 19 Jun, 2020, 02:31: PM

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