Finding (i)#tanAtanB#, (ii)#tan(A+B)#, (iii)#sin((A+B)/2)# using Addition Formulae?
Given #cos(A+B) = 3/5# and #cos A cos B = 7/10# , where A and B are both acute angles, find the value of
(i)#tanAtanB# ,
(ii)#tan(A+B)# ,
(iii)#sin((A+B)/2)# .
Answers:
(i) #1/7#
(ii) #3/4#
(iii) #sqrt(5)/5#
Given
(i)
(ii)
(iii)
Answers:
(i)
(ii)
(iii)
2 Answers
Those are right except (ii) is inverted.
Explanation:
Fun. Given
Let's review the relevant identities.
One double angle formula is
The average of
One of three wrong, B-.
Kindly refer to the Explanation Section.
Explanation:
Given that
Hence,
Given that,
Adding,
But,
Now,
Finally, to find
Since,