Question

CosA + sinA= sinA+cosA
____ ____
1-tanA 1-cotA

Answer 1

Step-by-step explanation:

We have,

(1+tan

2

A)

2

tanA

+

(1+cot

2

A)

2

cotA

=

(sec

2

A)

2

tanA

+

(cosec

2

A)

2

cotA

+

(cosec

2

A)

2

cotA

∵1+tan

2

A=sec

2

A and 1+cot

2

A=cosec

2

A

=

sec

4

A

cosA

sinA

+

cosec

4

A

sinA

cosA

=

cos

4

A

1

cosA

sinA

+

sin

4

A

1

sinA

cosA

=

cosA

sinA

×

1

cos

4

A

+

sinA

cosA

×

1

sin

4

A

=sinAcos

3

A+cosAsin

3

A

=sinAcosA(cos

2

A+sin

2

A) ∵cos

2

A+sin

2

A=1

=sinAcosA

Hence proved that ;

(1+tan

2

A)

2

tanA

+

(1+cot

2

A)

cotA

=sinAcosA