Question

prove that sec A(1-sin A)(sec A+ tan A)=1​

Answer 1

Step-by-step explanation:

L.H.S=secA(1−sinA)(secA+tanA)=(secA−

cosA

sinA

)(secA+tanA)

=(secA−tanA)(secA+tanA)

=sec

2

A−tan

2

A

Putting if tan

2

A+1=sec

2

A−

we get L.H.S=1+tan

2

A−tan

2

A=1

⇒L.H.S=R.H.S

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Answer 2

Answer:

L.H.S=secA(1−sinA)(secA+tanA)=(secA−cosAsinA)(secA+tanA)

=(secA−tanA)(secA+tanA)

=sec2A−tan2A

Putting if tan2A+1=sec2A−

we get L.H.S=1+tan2A−tan2A=1

⇒L.H.S=R.H.S

secA+tanA

secA−tanA

=

(1+sinA)

2

cos

2

A