Question

Check and discuss the above relations in the case of angles between 0° and 90°, whether they hold for these angles or not ? So,

( 1 ) sin (90° - A) = cos A

( 2 ) cos (90° - A) = sin A

( 3 ) tan (90° - A) = cot A

( 4 ) cot (90° - A) = tan A

( 5 ) sec (90° - A) = cosec A

( 6 ) cosec (90° - A) = sec A​

Answer 1

QUESTION :-

Check and discuss the above relations in the case of angles between 0° and 90°, whether they hold for these angles or not ? So,

( 1 ) sin (90° - A) = cos A

( 2 ) cos (90° - A) = sin A

( 3 ) tan (90° - A) = cot A

( 4 ) cot (90° - A) = tan A

( 5 ) sec (90° - A) = cosec A

( 6 ) cosec (90° - A) = sec A

SOLUTION :-

• Let A = 30°

( 1 ) sin (90° - A) = cos A

⇒ sin (90° - 30°) = cos 30°

⇒ sin 60° = cos 30° = √3/2

( 2 ) cos (90° - A) = sin A

⇒ cos (90° - 30°) = sin 30°

⇒ cos 60° = sin 30° = 1/2

( 3 ) tan (90° - A) = cot A

⇒ tan (90° - 30°) = cot 30°

⇒ tan 60° = cot 30° = √3

( 4 ) cot (90° - A) = tan A

⇒ cot (90° - 30°) = tan 30°

⇒ cot 60° = tan 30° = 1/√3

( 5 ) sec (90° - A) = cosec A

⇒ sec (90° - 30°) = cosec 30°

⇒ sec 60° = cosec 30° = 2

( 6 ) cosec (90° - A) = sec A

⇒ cosec (90° - 30°) = sec 30°

⇒ cosec 60° = sec 30° = 2/√3

So, the above relations hold for all the

angles between 0° and 90°.

Answer 2

this is your answer think and discuss page no 286