Show that the coordinates of the orthocentre of `DeltaABC` is : `((x_1 a sec A + x_2 b sec B + x_3 c sec C)/(a sec A + b sec B + c sec A)), (y_1 a sec A + y_2 b sec B + y_3 c sec C)/(a sec A + b sec B + c sec C))`

Prove the following identities : (sec A)/ (sec A + 1) + (sec A)/ (sec A - 1) = 2 cosec^(2) A

If cosec A + sec A = cosec B + sec B , prove that tan A tan B = cot( A+ B)/ 2

sec^4 A− sec^ 2 A is equal to

sec 72 ^(@) - sec 36^(@) = 2.

Prove the following identities : cot^(2) A ((sec A - 1)/(1 + sin A)) + sec ^(2) A ((sin A -1)/ (1 + sec A)) = 0

In Delta ABC , angle B = 90 ^(@) Evaluate : cosec A cos C - sin A sec C .

sec^2 A+ sec^2(\pi /2- A) = sec^2A sec^2(\pi/2 -A)

Figure given here shows the variation of velocity of a particle with time. Find the following: (i) Displacement during the time intervals. (a) 0 to 2 sec., (b) 2 to 4 sec. and (c) 4 to 7 sec (ii) Accelerations at (a)t = 1 sec, (b) t = 3 sec. and (c)t = 6 sec. (iii) Average acceleration (a) between t = 0 to t = 4 sec. (b) between t = 0 to t = 7 sec. (iv) Average velocity during the motion.

Prove that in an acute angled triangle ABC , sec A+sec B +sec Cge 6 .

The value of int(sec x (2 + sec x))/((1+2 sec x)^(2))dx , is equal to