In any ΔABC, prove that a 2 sin ( B – C ) = (b2 – c 2 ) sin A

In any ΔABC, prove that a sin A – b sin B = c sin (A – B)

In any ΔABC, prove that Answer :

In any ΔABC, prove that Answer :

In any ΔABC, prove that ac cos B – bc cos A = (a2 – b 2 )

In any ΔABC, prove that a(b cos C – c cos B) = (b2 – c 2 )

By giving a counter-example, show that the following statement is false : p : If all the sides of a triangle are equal, then the triangle is obtuse angled.

Use contradiction method to prove that :

By giving a counter-example, show that the statement is false :
p : If n is an odd positive integer, then n is prime.

Consider the statement :
q : For any real numbers a and b, a2 = b2⇒ a = b
By giving a counter-example, prove that q is false.

Let p : If x is an integer and x2 is even, then x is even, Using the method of contrapositive, prove that p is true.

write each of the following using ‘if and only if’ :
(i) In order to get A grade, it is necessary and sufficient that you do all the homework regularly.
(ii) If you watch television, then your mind is free, and if your mind is free, then you watch television.