Question

The value of cos-A +1/1+cot A

​

Answer 1

Step-by-step explanation:

1+sinA

cosA

=

cot(

2

A

)+1

cot(

2

A

)−1

LHS:-

(1+sinA)

cosA

=

1+2(cosA/2)sin(A/2)

2cos

2

(A/2)−1

=

cos

2

(A/2)+sin

2

(A/2)+2cos(A/2)sin(A/2)

cos

2

A/2+cos

2

A/2−1

=

(cot(A/2)+sinA/2)

2

cos

2

(A/2)−sin

2

(A/2)

=

(cos(A/2)+sin(A/2))

2

(cosA/2+sinA/2)(cosA/2−sinA/2)

=

cosA/2+sinA/2

cosA/2−sinA/2

=

sinA/2[cotA/2+1]

sinA/2[cotA/2−1]

=[

cot(A/2)+1

cot(A/2)−1

]=RHs

∴LHS=RHS.