Question

Question:-

Cos A - Sin A+ 1 / Cos A + Sin A- 1 = Cosec A + Cot A , Using identity cosec² A = 1 + cot² A​

Answer 1

Using cos2x=2cos

2

x−1⇒cos

2

x=

2

cos2x+1

I=cos

2

A+cos

2

B+cos

2

C

=

2

1

(cos2A+cos2B+cos2C+3)

Now, from A+B+C=180⇒2C=360−2(A+B)

We get

I=

2

1

(2cos(A+B)cos(A−B)+cos(360−2(A+B))+3)

=

2

1

(2cos(A+B)cos(A−B)+cos(2(A+B))+3)

=

2

1

(2cos(A+B)cos(A−B)+2cos

2

(A+B)−1+3)

=

2

1

[2cos(180−C)(cos(A+B)+cos(A−B))+2]

=

2

1

[−2cosC(2cosAcosB)+2]

=1−2cosAcosBcosC