Question

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

Answer 1

Step-by-step explanation:

We need to find value of (secA+tanA)(1−sinA)

Putting the values of secA and tanA as

secA=

cosA

1

tanA=

cosA

sinA

(

cosA

1

+

cosA

sinA

)(1−sinA)

=

cosA

1+sinA

(1−sinA)

=

cosA

1−sin

2

A

=

cosA

cos

2

A

.... (As 1−sin

2

A=cos

2

A)

=cosA

Answer 2

(Sec A + tan A) (1 - sin A) = sec A + tan A - sec A × sin A - tan A × sin A

= (1/cos A)+tan A-(1/cosA)(sin A)-(sin² A/cos A)

=[(1-sin²A) /cos A] +tan A - tan A

= cos²A/cos A

= cos A

Proved