Find sin(a+B) cos a = 5/13, with a in quadrant I
tanB = 4/3 with B in quadrant 4.
Give exact answer, not decimal approximation.

sin(a+B)=

Cos A=5/13

we have

Cos² A=

25/169=1-Sin²A

sin²A=1-25/169

sin²A=144/169

Sin A=

again

Tan B=4/3

P/b=4/3

p=4

b=3

h=

Now

Sin B=p/h=4/5

in IV quadrant sin angle is negative so

Sin B=-4/5

CosB=b/h=3/5

Now

Sin(A+B):sinAcosB+CosAsinB

now

substitute value

Sin(A+B):12/13*3/5+5/13*(-4/5)=36/65-4/13

=16/65 is a required answer

your answer is -9

step-by-step explanation:

the correct answer option is (2x-3)(2x+3).

step-by-step explanation:

we are given the following expression and we are to factorize it:

we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.

the two such factors of 36 are negative six and postive six.

factorizing the given expression to get:

therefore, the correct factorization of is (2x-3)(2x+3).