Question

( Seca + tana) ( 1 - Sina)

Answer 1

Seca+tana=(1+sina)/Cosa
(sec a+tana)(1-sina)=
$1 - {sin }^{2} a \div \cos( a) \\ {cos}^{2} \div cosa$
cosa

Answer 2

Sec A=1/cosA
Tan A=sinA/CosA
Now
SecA+TanA=(1/CosA+Sin/Cos)
=(1+sinA)/cosA
Now
Lhs=(1+sinA)(1-sinA)/CosA
=(1-sin²A)/cosA. ........(∵(a+b)(a-b)=a²-b² )
=cos²A/cosA. ........[(1-sin²)=cos²a because sin²a+cos²a=1]
=Cos A




Hope it helps..!
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