Find the exact value of sin alpha beta if sin alpha 45 and

Find the exact value of sin (alpha + beta) if sin alpha = -4/5 and sin beta = -5/13, with alpha in quadrant IV and B in quadrant III sin (alpha + B) = Use Identities to simplify cos^2 B - 8 sin^2 B/1 - 9 sin^2 B = Determine if equation is positive negative or both signs make the equation correct sin 146.0 degree = plusminus squareroot 1 - cos 292 degree/2 Simplify csc x/cos x + sec x/sin x What is the sum. 2 pi/6 + pi/4 =

Solution

3)given sina =-4/5, sinb =-5/13

cosa=((5²-4²))/5 =3/5

cosb=-((13²-5²))/13 =-12/13

sin(a+b)=sinacosb +cosasinb

=(-4/5)(-12/13) +(3/5)(-5/13)

=(48/65)-(15/65)

=33/65

B) (cos²B-8sin²B)/(1-9sin²B)

we know ,sin²B+cos²B=1 is an identity =>cos²B=1-sin²B

= ((1-sin²B)-8sin²B)/(1-9sin²B)

=(1-9sin²B)/(1-9sin²B)

=1

c)sin146^o=+[(1-cos292^o)/2]

d)(cscx/cosx)+(secx/sinx)

=((1/sinx)/cosx)+((1/cosx)/sinx)

=(1/(sinxcosx))+(1/(sinxcosx))

=2/(sinxcosx)

=2 cscx secx

E)(2pi/6)+(pi/4)

=(pi/3)+(pi/4)

=(4pi +3pi)/13

=7pi/12