Prove that: (i) sin 70∘cos 20∘+cosec 20∘sec 70∘−2 cos 70∘

1.	Prove that: (i) sin 70∘cos 20∘+cosec 20∘sec 70∘−2 cos 70∘ cosec 20∘=0 (ii) cos 80∘sin 10∘+cos 59∘ cosec 31∘=2 (iii) 2 sin 68∘cos 22∘−2 cot 15∘5 tan 75∘−3 tan 45∘ tan 20∘ tan 40∘ tan 50∘ tan 70∘5=1 (iv) sin 18∘cos 72∘+√3(tan 10∘ tan 30∘ tan 40∘ tan 50∘ tan 80∘)=2 (v) 7 cos 55∘3 sin 35∘−4(cos 70∘ cosec 20∘)3(tan 5∘ tan 25∘ tan 45∘ tan 65∘ tan 85∘)=1
Answer» Prove that: (i) $\frac{s i n 70^{\circ}}{c o s 20^{\circ}} + \frac{c o s e c 20^{\circ}}{s e c 70^{\circ}} - 2 c o s 70^{\circ} c o s e c 20^{\circ} = 0$ (ii) $\frac{c o s 80^{\circ}}{s i n 10^{\circ}} + c o s 59^{\circ} c o s e c 31^{\circ} = 2$ (iii) $\frac{2 s i n 68^{\circ}}{c o s 22^{\circ}} - \frac{2 c o t 15^{\circ}}{5 t a n 75^{\circ}} - \frac{3 t a n 45^{\circ} t a n 20^{\circ} t a n 40^{\circ} t a n 50^{\circ} t a n 70^{\circ}}{5} = 1$ (iv) $\frac{s i n 18^{\circ}}{c o s 72^{\circ}} + \sqrt{3} (t a n 10^{\circ} t a n 30^{\circ} t a n 40^{\circ} t a n 50^{\circ} t a n 80^{\circ}) = 2$ (v) $\frac{7 c o s 55^{\circ}}{3 s i n 35^{\circ}} - \frac{4 (c o s 70^{\circ} c o s e c 20^{\circ})}{3 (t a n 5^{\circ} t a n 25^{\circ} t a n 45^{\circ} t a n 65^{\circ} t a n 85^{\circ})} = 1$

Prove that: (i) sin 70∘cos 20∘+cosec 20∘sec 70∘−2 cos 70∘ cosec 20∘=0 (ii) cos 80∘sin 10∘+cos 59∘ cosec 31∘=2 (iii) 2 sin 68∘cos 22∘−2 cot 15∘5 tan 75∘−3 tan 45∘ tan 20∘ tan 40∘ tan 50∘ tan 70∘5=1 (iv) sin 18∘cos 72∘+√3(tan 10∘ tan 30∘ tan 40∘ tan 50∘ tan 80∘)=2 (v) 7 cos 55∘3 sin 35∘−4(cos 70∘ cosec 20∘)3(tan 5∘ tan 25∘ tan 45∘ tan 65∘ tan 85∘)=1

Answer»

Prove that:

(i) $\frac{s i n 70^{\circ}}{c o s 20^{\circ}} + \frac{c o s e c 20^{\circ}}{s e c 70^{\circ}} - 2 c o s 70^{\circ} c o s e c 20^{\circ} = 0$

(ii) $\frac{c o s 80^{\circ}}{s i n 10^{\circ}} + c o s 59^{\circ} c o s e c 31^{\circ} = 2$

(iii) $\frac{2 s i n 68^{\circ}}{c o s 22^{\circ}} - \frac{2 c o t 15^{\circ}}{5 t a n 75^{\circ}} - \frac{3 t a n 45^{\circ} t a n 20^{\circ} t a n 40^{\circ} t a n 50^{\circ} t a n 70^{\circ}}{5} = 1$

(iv) $\frac{s i n 18^{\circ}}{c o s 72^{\circ}} + \sqrt{3} (t a n 10^{\circ} t a n 30^{\circ} t a n 40^{\circ} t a n 50^{\circ} t a n 80^{\circ}) = 2$

(v) $\frac{7 c o s 55^{\circ}}{3 s i n 35^{\circ}} - \frac{4 (c o s 70^{\circ} c o s e c 20^{\circ})}{3 (t a n 5^{\circ} t a n 25^{\circ} t a n 45^{\circ} t a n 65^{\circ} t a n 85^{\circ})} = 1$

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