Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.

(i) sin67° + cos75°
(ii) cot65° + tan49°
(iii) sec78° + cosec56°
(iv) cosec54° + sin72°

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Solution

$(i) \sin 67 ° + \cos 75 ° = \cos (90 ° - 67 °) + \sin (90 ° - 75 °) = \cos 23 ° + \sin 15 °$

$(ii) \cot 65 ° + \tan 49 ° = \tan (90 ° - 65 °) + \cot (90 ° - 49 °) = \tan 25 ° + \cot 41 °$

$(iii) \sec 78 ° + cosec 56 ° = \sec (90 ° - 12 °) + cosec (90 ° - 34 °) = cosec 12 ° + \sec 34 °$

$(iv) cosec 54 ° + \sin 72 ° = \sec (90 ° - 54 °) + \cos (90 ° - 72 °) = \sec 36 ° + \cos 18 °$

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Express each of the following in terms of T-ratios of angles lying between $0^{\circ} a n d 45^{\circ} :$

(i) $s i n 67^{\circ} + c o s 75^{\circ}$ (ii) $c o t 65^{\circ} + t a n 49^{\circ}$

(iii) $s e c 78^{\circ} + c o s e c 56^{\circ}$ (iv) $c o s e c 54^{\circ} + s i n 72^{\circ}$

Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

s i n 67^{\circ} + c o s 75^{\circ}

0^{\circ}

45^{\circ}

0^{\circ}

45^{\circ}

cot 85^{\circ} + cos 75^{\circ}

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