Question

Sum based on trigonometry:
Prove that :
1+sinA/cosA=1+sinA+cosA/1+cosA-sinA​

Answer 1

Answer:

We have,

1+csosA−sinA

1+cosA+sinA

=

1+cosA−sinA

1+cosA+sinA

×

(1+cosA)+sinA

(1+cosA)+sinA

=

(1+cosA)

2

−sin

2

A

((1+cosA)+sinA)

2

=

1+cos

2

A+2cosA−1+cos

2

A

(1+cosA)

2

+sin

2

A+2(1+cosA)sinA

=

2cos

2

A+2cosA

1+cos

2

A+sin

2

A+2cosA+2sinA+2sinAcosA

=

2cos

2

A+2cosA

1+cos

2

A+sin

2

A+2cosA+2sinA+2sinAcosA

2cosA(1+cosA)

1+1+2cosA+2sinA+2sinAcosA

2cosA(1+cosA)

2+2cosA+2sinA+2sinAcosA

cosA(1+cosA)

1+cosA+sinA+sinAcosA

=

cosA(1+cosA)

1+sinA+cosA(1+sinA)

=

cosA(1+cosA)

(1+sinA)(1+cosA)

=

cosA

1+sinA

Hence proved.