
answers:
MyRank say: a. sin3x/sinxcosx = 4cosx  secx
4cosx  secx
4/secx  1/cosx
4cosx  secx / secxcosx
Sin3x/sinxcosx.
b. 1+sec(φ) / sin(φ) + tan(φ)
1+secφ/sinφtanφ
1+secφ / (sinφ+tanφ) = cose(φ).

Ash say: (a) sin3x / sinx cosx
= sin(x+2x) / sinx cosx
= (sinx cos2x + sin2x cosx) / sinx cosx
= (sinx (2cos²x  1) + (2 sinx cosx) cosx) / sinx cosx
= sinx((2cos²x  1 + 2 cos²x) / sinx cosx
= (4cos²x  1)/cosx
= 4cos²x/cosx  1/cosx
= 4cosx  secx
(b) There seems to be an error in your identity.
The RHS should be either csc(ø) or csc(ø) but NOT csc(ø)
I have solved for both possibilities.
(1+sec(ø)) / (sin(ø)+tan(ø))
= (1+sec(ø)) / (sin(ø)  tan(ø)
= (1+sec(ø)) / (sin(ø)  sin(ø)/cos(ø))
= (1+sec(ø)) / sin(ø)(1 + 1/cos(ø))
= (1+sec(ø)) / sin(ø)(1 + sec(ø))
= 1/sin(ø)
=  csc(ø)
OR
(1+sec(ø)) / (sin(ø)+tan(ø))
= (1+sec(ø)) / (sin(ø) + sin(ø)/cos(ø))
= (1+sec(ø)) / (sin(ø) (1 + 1/cos(ø))
= (1+sec(ø)) / (sin(ø) (1 + sec(ø))
= 1/sin(ø)
= csc(ø)

Bella say: izptjqrw

bidii say: vffpjelf
