Mathematics
Express each of the following in terms of angles between 0° and 45° :
(i) sin 59° + tan 63°
(ii) cosec 68° + cot 72°
(iii) cos 74° + sec 67°
Trigonometric Identities
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Answer
(i) Solving,
⇒ sin 59° + tan 63°
⇒ sin (90 - 31)° + tan (90 - 27)°
By formula,
sin (90° - A) = cos A and tan (90° - A) = cot A.
⇒ cos 31° + cot 27°.
Hence, sin 59° + tan 63° = cos 31° + cot 27°.
(ii) Solving,
⇒ cosec 68° + cot 72°
⇒ cosec (90 - 22)° + cot (90 - 18)°
By formula,
cosec (90° - A) = sec A and cot (90° - A) = tan A.
⇒ sec 22° + tan 18°.
Hence, cosec 68° + cot 72° = sec 22° + tan 18°.
(iii) Solving,
⇒ cos 74° + sec 67°
⇒ cos (90 - 16)° + sec (90 - 23)°
By formula,
cos (90° - A) = sin A and sec (90° - A) = cosec A.
⇒ sin 16° + cosec 23°.
Hence, cos 74° + sec 67° = sin 16° + cosec 23°.
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