Question

prove that √





= sec A + tan A​

Answer 1

Step-by-step explanation:

864

Question Bank Solutions 25930

Concept Notes & Videos 230

Time Tables 15

Syllabus

Advertisement Remove all ads

Sum

Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.

SOLUTION

L.H.S. = `sqrt(((1 - sin θ)(1 - sin θ))/((1 + sin θ)(1 - sin θ)))`

= `sqrt((1 + sin^2θ - 2sinθ)/(1 - sin^2θ)`

= `sqrt((1 + sin^2θ - 2sinθ)/(cos^2θ)`

= `sqrt( 1/cos^2θ + sin^2θ/cos^2θ - (2sin θ)/cos θ xx 1/cosθ`

= `sqrt( sec^2θ + tan^2 θ - 2 tan θ. sec θ)`

= `sqrt((sec θ - tan θ)^2)`

= sec θ - tan θ

= R.H.S.

Hence proved.

Answer 2

Answer

(1−sinA)

(1+sinA)

×

(1+sinA)

(1+sinA)

=

1−sin

2

A

(1+sinA)

2

=

cos

2

A

(1+sinA)

2

=

cosA

1+sinA

=

cosA

1

+

cosA

sinA =secA+tanA

Hence proved.

Flw_me!