Math, asked by katharsakshi24, 2 months ago

Prove that 1+SinA/cosA +CosA/1+SinA =2 Sec A

Answers

Answered by akhtarabegum

1

Step-by-step explanation:

LHS: 1+SinA/ CosA + CosA/ 1+ SinA

= (1+SinA)^2 + Cos^2A / ( CosA ) ( 1+SinA)

= 1+ Sin^2 A + 2SinA + 1 - Sin^2A / ( CosA ) ( 1+SinA)

= 2 + 2SinA / ( CosA )( 1+SinA)

= 2 ( 1+SinA) / ( CosA )( 1+SinA)

= 2 / cosA

= 2 sec A

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