00:00So in this case we are given
00:01and we are 2 acute angles
00:03which means a is also less than 90 degree
00:06and b is also less than 90 degree
00:08and we have given an relation
00:102a plus 2b is equal to pi
00:12and add the maximum value of
00:15sin a multiplied by sin b
00:18so first of all we will take 2 common
00:21then it will become
00:22a plus b is equal to
00:242 goes in this side on the RHS
00:27in divide pi by 2
00:29pi by 2 means 90 degree
00:30we will put here 90 degree
00:32from this equation if we take b to the right side
00:35it will become a is equal to 90 degree minus b
00:39now we will imply the formula
00:41sin a minus b
00:43here compare with this formula of trigonometry
00:47sin a minus b is equal to
00:49sin a cos b minus cos sin b
00:51put the value here a is 90 degree
00:54and b is b
00:55so if we simplify after putting value
00:58this becomes sin 90
01:00sin 90 cos b minus cos 90 sin b
01:06the value of cos 90 and sin b is
01:10cos 90 degree is 0
01:12and if we multiply anything by 0
01:14that also becomes 0
01:16minus 0
01:17if we subtract 0 from something
01:20then that thing don't change
01:22and sin b on outside
01:24now sin 90 degree value is 1
01:28replace it by 1
01:30it becomes 1
01:32so cos b into sin b
01:35cos b sin b
01:36we know the formula sin 2 theta is equal to 2 sin theta cos theta
01:41if we take to the left side
01:44it becomes sin 2 theta upon me 2 is equal to sin theta cos theta
01:49compare put b in place of theta
01:52which become sin 2 b upon me 2 is equal to sin b cos b
01:58sin 5 cos b cos b
02:00cos b cos b and cos b sin b are same
02:02so sin 2 b upon 2
02:05then sin 2 b maximum value is 0
02:08any function of sin 1
02:10sin theta here we can consider to be theta or any angle
02:14sin theta here we can consider theta est and eigen 4
02:15the maximum value of sin function can be 1
02:18so the maximum value of upper version 0
02:20will be 1 and below 1 is 2 constant 0
02:24So its maximum value will be 1 upon 2.
02:27So here comes the final answer.
02:30Maximum value of sine A dot sine B is 1 upon 2 half.
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