Prove that: (i)cos(2π+θ)cosec(2π+θ)tan(π/2+θ)sec(π/2+θ)cosθco

1.	Prove that: (i)cos(2π+θ)cosec(2π+θ)tan(π/2+θ)sec(π/2+θ)cosθcot(π+θ)=1 (ii)cosec(90∘+θ)+cot(450∘+θ)cosec(90∘−θ)+tan(180∘−θ)+tan(180∘+θ)+sec(180∘−θ)tan(360∘+θ)−sec(−θ)=2 (iii)sin(180∘+θ)cos(90∘+θ)tan(270∘−θ)cot(360∘−θ)sin(360∘−θ)cos(360∘+θ)cosec(−θ)sin(270∘+θ)(iv)1+cotθ−sec(π2+θ)}1+cotθ+sec(π2+θ)}=2cotθ (v)tan(90∘−θ)sec(180∘−θ)sin(−θ)sin(180∘+θ)cot(360∘−θ)cosec(90∘−θ)=1
Answer» Prove that: $(i) \frac{c o s (2 π + θ) c o s e c (2 π + θ) t a n (π / 2 + θ)}{s e c (π / 2 + θ) c o s θ c o t (π + θ)} = 1$ $(i i) \frac{c o s e c (90^{\circ} + θ) + c o t (450^{\circ} + θ)}{c o s e c (90^{\circ} - θ) + t a n (180^{\circ} - θ)} + \frac{t a n (180^{\circ} + θ) + s e c (180^{\circ} - θ)}{t a n (360^{\circ} + θ) - s e c (- θ)} = 2$ $(i i i) \frac{s i n (180^{\circ} + θ) c o s (90^{\circ} + θ) t a n (270^{\circ} - θ) c o t (360^{\circ} - θ)}{s i n (360^{\circ} - θ) c o s (360^{\circ} + θ) c o s e c (- θ) s i n (270^{\circ} + θ)} (i v) 1 + c o t θ - s e c (\frac{π}{2} + θ)} 1 + c o t θ + s e c (\frac{π}{2} + θ)} = 2 c o t θ$ $(v) \frac{t a n (90^{\circ} - θ) s e c (180^{\circ} - θ) s i n (- θ)}{s i n (180^{\circ} + θ) c o t (360^{\circ} - θ) c o s e c (90^{\circ} - θ)} = 1$

Prove that: (i)cos(2π+θ)cosec(2π+θ)tan(π/2+θ)sec(π/2+θ)cosθcot(π+θ)=1 (ii)cosec(90∘+θ)+cot(450∘+θ)cosec(90∘−θ)+tan(180∘−θ)+tan(180∘+θ)+sec(180∘−θ)tan(360∘+θ)−sec(−θ)=2 (iii)sin(180∘+θ)cos(90∘+θ)tan(270∘−θ)cot(360∘−θ)sin(360∘−θ)cos(360∘+θ)cosec(−θ)sin(270∘+θ)(iv)1+cotθ−sec(π2+θ)}1+cotθ+sec(π2+θ)}=2cotθ (v)tan(90∘−θ)sec(180∘−θ)sin(−θ)sin(180∘+θ)cot(360∘−θ)cosec(90∘−θ)=1

Answer»

Prove that:

$(i) \frac{c o s (2 π + θ) c o s e c (2 π + θ) t a n (π / 2 + θ)}{s e c (π / 2 + θ) c o s θ c o t (π + θ)} = 1$

$(i i) \frac{c o s e c (90^{\circ} + θ) + c o t (450^{\circ} + θ)}{c o s e c (90^{\circ} - θ) + t a n (180^{\circ} - θ)} + \frac{t a n (180^{\circ} + θ) + s e c (180^{\circ} - θ)}{t a n (360^{\circ} + θ) - s e c (- θ)} = 2$

$(i i i) \frac{s i n (180^{\circ} + θ) c o s (90^{\circ} + θ) t a n (270^{\circ} - θ) c o t (360^{\circ} - θ)}{s i n (360^{\circ} - θ) c o s (360^{\circ} + θ) c o s e c (- θ) s i n (270^{\circ} + θ)} (i v) 1 + c o t θ - s e c (\frac{π}{2} + θ)} 1 + c o t θ + s e c (\frac{π}{2} + θ)} = 2 c o t θ$

$(v) \frac{t a n (90^{\circ} - θ) s e c (180^{\circ} - θ) s i n (- θ)}{s i n (180^{\circ} + θ) c o t (360^{\circ} - θ) c o s e c (90^{\circ} - θ)} = 1$

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