Question

Express the trigonometry ratios sin A, secA and tan A in term of Cot A​

Answer 1

Answer:

sinA = 1/√(1+cot²A)

secA = (cot²A+1)/cot²A

tanA = 1/cotA

Answer 2

Answer:

sinA=

cot

2

A+1

1

secA=

cotA

cot

2

A+1

tanA=

cotA

1

We have

1]cosec

2

A−cot

2

A=1

⇒cosec

2

A=1+cot

2

A

⇒(cosecA)

2

=cot

2

A+1

⇒(

sinA

1

)

2

=cot

2

+1

⇒(sinA)

2

=

cot

2

A+1

1

⇒sinA=±

cot

2

A+1

1

We reject the negative value of sinA for acute angle A. Therefore sinA=

cot

2

A+1

1

2]tanA=

cotA

1

3]We have sec

2

A−tan

2

A=1

⇒sec

2

A=1+tan

2

A

⇒sec

2

A=1+

cot

2

A

1

=

cot

2

A

cot

2

A+1

⇒secA=

cotA

cot

2

A+1