Question

prove that: (secA+tanA)(1-sinA)=cosA​

Answer 1

Answer:

L. H. S.

=> (1/cos A + Sin A / cos A) ( 1 - Sin A)

=> [ (1 + sin A ) / cos A] ( 1 - Sin A)

=> ( 1 - sin^2 A) / cos A

=> Cos^2 A / cos A

=> Cos A

=> R. H. S.

Hence, Proved.

Answer 2

Answer:

LHS = RHS = cosA

Step-by-step explanation:

LHS = (secA + tanA) (1 - sinA)

= [(1/cosA) + (sinA/cosA)] × (1- sinA)

= [(1+ sinA)/cosA] (1- sinA)

= [(1+ sinA) (1- sinA)/cosA]

= 1^2 - sin^2A/cosA

[°.° a^2 - b^2 = (a + b)(a - b)]

= 1 - sin^2A/cosA

= cos^2A/cosA

= cosA = RHS

.°. LHS = RHS

Hence, it is proved.

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