Prove that: (i) sin(70∘+θ)−cos(20∘−θ)=0 (ii) tan(55∘−θ)

1.	Prove that: (i) sin(70∘+θ)−cos(20∘−θ)=0 (ii) tan(55∘−θ)−cot(35∘+θ)=0 (iii) cosec(67∘+θ)−sec(23∘−θ)=0 (iv) cosec(65∘+θ)−sec(25∘−θ)−tan(55∘−θ)+cot(35∘+θ)=0 (v) sin(50∘+θ)−cos(40∘−θ)+tan 1∘ tan 10∘ tan 80∘ tan 89∘=1
Answer» Prove that: (i) $s i n (70^{\circ} + θ) - c o s (20^{\circ} - θ) = 0$ (ii) $t a n (55^{\circ} - θ) - c o t (35^{\circ} + θ) = 0$ (iii) $c o s e c (67^{\circ} + θ) - s e c (23^{\circ} - θ) = 0$ (iv) $c o s e c (65^{\circ} + θ) - s e c (25^{\circ} - θ) - t a n (55^{\circ} - θ) + c o t (35^{\circ} + θ) = 0$ (v) $s i n (50^{\circ} + θ) - c o s (40^{\circ} - θ) + t a n 1^{\circ} t a n 10^{\circ} t a n 80^{\circ} t a n 89^{\circ} = 1$

Prove that: (i) sin(70∘+θ)−cos(20∘−θ)=0 (ii) tan(55∘−θ)−cot(35∘+θ)=0 (iii) cosec(67∘+θ)−sec(23∘−θ)=0 (iv) cosec(65∘+θ)−sec(25∘−θ)−tan(55∘−θ)+cot(35∘+θ)=0 (v) sin(50∘+θ)−cos(40∘−θ)+tan 1∘ tan 10∘ tan 80∘ tan 89∘=1

Answer»

Prove that:

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

(ii) $t a n (55^{\circ} - θ) - c o t (35^{\circ} + θ) = 0$

(iii) $c o s e c (67^{\circ} + θ) - s e c (23^{\circ} - θ) = 0$

(iv) $c o s e c (65^{\circ} + θ) - s e c (25^{\circ} - θ) - t a n (55^{\circ} - θ) + c o t (35^{\circ} + θ) = 0$

(v) $s i n (50^{\circ} + θ) - c o s (40^{\circ} - θ) + t a n 1^{\circ} t a n 10^{\circ} t a n 80^{\circ} t a n 89^{\circ} = 1$

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Prove that: (i) sin(70∘+θ)−cos(20∘−θ)=0 (ii) tan(55∘−θ)−cot(35∘+θ)=0 (iii) cosec(67∘+θ)−sec(23∘−θ)=0 (iv) cosec(65∘+θ)−sec(25∘−θ)−tan(55∘−θ)+cot(35∘+θ)=0 (v) sin(50∘+θ)−cos(40∘−θ)+tan 1∘ tan 10∘ tan 80∘ tan 89∘=1

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