1 of 2

Q.1) Express the trigonometric ratios sin A, sec A and tan A

in terms of cot A.

EXERCISE 8.4

Solution:

tan A =

1

cot A

sec2A = 1 + tan2A

1

+

1

cot A

2

=

sec2A

1

+

1

cot2A

=

sec2A

∴

∴

sec A

=

 

cot A

∴

[Taking square roots]

… (i)

[From (i)]

sec2A

=

1 + cot2A

cot2A

∴

… (ii)

2 of 2

Q.1) Express the trigonometric ratios sin A, sec A and tan A

in terms of cot A.

EXERCISE 8.4

Solution:

tan A =

1

cot A

sec A

=

 

cot A

cos A =

1

sec A

1

÷

 

cot A

=

cos A =

 

 

tan A =

sin A

cos A

sin A

=

tan A ×cos A

=

1

cot A

×

 

 

sin A

∴

=

 

 

∴

∴

[From (ii)]

… (iii)

[From (i) and (iii)]

… (i)

… (ii)