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Question Number 51905 Answers: 2 Comments: 0

If p = cos θ + i sinθ and q = cos φ + i sin φ Show that: (i) ((p − q)/(p + q)) = i tan (((θ − φ)/2)) (ii) (((p + q)(pq − 1))/((p − q)(pq + 1))) = ((sin θ + sin φ)/(sin θ − sin φ))

$If p = \cos θ + i \sin θ and q = \cos ϕ + i \sin ϕ$ $Show that :$ $(i) \frac{p - q}{p + q} = i \tan (\frac{θ - ϕ}{2})$ $(ii) \frac{(p + q) (pq - 1)}{(p - q) (pq + 1)} = \frac{\sin θ + \sin ϕ}{\sin θ - \sin ϕ}$

Question Number 51884 Answers: 1 Comments: 4

Question Number 51849 Answers: 3 Comments: 3

Question Number 51700 Answers: 1 Comments: 1

Question Number 51658 Answers: 3 Comments: 7

Question Number 51636 Answers: 1 Comments: 4

Question Number 51644 Answers: 0 Comments: 0

Question Number 51605 Answers: 0 Comments: 0

Question Number 51558 Answers: 1 Comments: 3

Question Number 51549 Answers: 0 Comments: 0

A and B are two points from the plan (P) with AB=4 define and draw the locus of points M ∈(P) wich verify MA +MB =8 .

$A a n d B a r e t w o p o i n t s f r o m t h e p l a n (P) w i t h A B = 4 d e f i n e a n d d r a w$ $t h e l o c u s o f p o i n t s M \in (P) w i c h v e r i f y M A + M B = 8 .$

Question Number 51502 Answers: 0 Comments: 1

Question Number 51466 Answers: 1 Comments: 5

Question Number 51245 Answers: 2 Comments: 0

Question Number 51141 Answers: 1 Comments: 0

Question Number 51088 Answers: 2 Comments: 1

Question Number 50829 Answers: 2 Comments: 1

Question Number 50762 Answers: 1 Comments: 1

Question Number 50674 Answers: 2 Comments: 3

Find the maximum area of a triangle inscribed in an ellipse with parameters a and b.

$F i n d t h e m a x i m u m a r e a o f a t r i a n g l e$ $i n s c r i b e d i n a n e l l i p s e w i t h p a r a m e t e r s$ $a a n d b .$

Question Number 50577 Answers: 1 Comments: 1

Question Number 50561 Answers: 3 Comments: 1

Question Number 50460 Answers: 2 Comments: 2

Question Number 50352 Answers: 1 Comments: 5

The distances from a point to the sides of a triangle are p,q,r. Find the maximum (or minimum) area of the triangle, if it exists. Assume r≤q≤p.

$T h e d i s t a n c e s f r o m a p o i n t t o t h e s i d e s$ $o f a t r i a n g l e a r e p, q, r . F i n d t h e$ $m a x i m u m (o r m i n i m u m) a r e a o f t h e$ $t r i a n g l e, i f i t e x i s t s .$ $A s s u m e r ⩽ q ⩽ p .$

Question Number 49987 Answers: 1 Comments: 4

Question Number 49984 Answers: 1 Comments: 1

Question Number 49970 Answers: 2 Comments: 1

Question Number 49830 Answers: 3 Comments: 1

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