Express each of the following in terms of trigonometric ratios of angles between 0- and 45- i sin 75-cosec 75-ii tan 65-cot 49-iii sec 67-cosec 58-iv cos 83- - sec 76- -4 MARKS-

Solution: 1 Mark each (i) sin 75^∘+cosec 75^∘ = sin (90^∘ 15^∘) + cosec(90^∘ 15^∘) =(cos 15^∘+sec 15^∘) (ii) tan 65^∘+cot 49^∘ = tan(90^∘ 25^∘) + cot(90^∘ ...

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Byju's Answer

Standard IX

Mathematics

Relationship between Trigonometric Ratios

Express each ...

Question

Express each of the following in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$

$(i) s i n 75^{\circ} + c o s e c 75^{\circ}$

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

$(i i i) s e c 67^{\circ} + c o s e c 58^{\circ}$

$(i v) c o s 83^{\circ} - s e c 76^{\circ}$ [4 MARKS]

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Solution

Solution: 1 Mark each

$(i) s i n 75^{\circ} + c o s e c 75^{\circ}$

$= s i n (90^{\circ} - 15^{\circ}) + c o s e c (90^{\circ} - 15^{\circ})$

$= (c o s 15^{\circ} + s e c 15^{\circ})$

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

$= t a n (90^{\circ} - 25^{\circ}) + c o t (90^{\circ} - 41^{\circ})$

$= (c o t 25^{\circ} + t a n 41^{\circ})$

$(i i i) s e c 67^{\circ} + c o s e c 58^{\circ}$

$= s e c (90^{\circ} - 23^{\circ}) + c o s e c (90^{\circ} - 32^{\circ})$

$= (c o s e c 23^{\circ} + s e c 32^{\circ})$

$(i v) c o s 83^{\circ} - s e c 76^{\circ}$

$= c o s (90^{\circ} - 7^{\circ}) - s e c (90^{\circ} - 14^{\circ})$

$= (s i n 7^{\circ} - c o s e c 14^{\circ})$

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Similar questions

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°

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

(i) sin 59° + cos 56°
(ii) tan 65° + cot 49°
(iii) sec 76° + cosec 52°
(iv) cos 78° + sec 78°
(v) cosec 54° + sin 72°
(vi) cot 85° + cos 75°
(vii) sin 67° + cos 75°

Express $(s i n 75^{\circ} + c o s e c 75^{\circ})$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $15^{\circ} .$

Q. Express

(c o s 83^{\circ} - s e c 76^{\circ})

in terms of trigonometric ratios of angles between

0^{\circ}

and

45^{\circ} .

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) $c o s e c 54^{\circ} + s i n 72^{\circ}$

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Express each of the following in terms of trigonometric ratios of angles between 0∘ and 45∘ (i)sin 75∘+cosec 75∘ (ii)tan 65∘+cot 49∘ (iii)sec 67∘+cosec 58∘ (iv)cos 83∘−sec 76∘ [4 MARKS]