Question

cos(3pi/2+a)sin(p+a)-tg(pi\\2+a)tg(2pi+a)

Answer 1

cos(3pi/2+a)sin(p+a)-tg(pi2+a)tg(2pi+a)=>

cos(3pi/2+a)=sin a

sin(p+a)=-sin a

tg(pi2+a)=-ctg a

tg(2pi+a)=tg a

(sin a)(-sin a)-(-ctg a)(tg a)= -sin^{2}a +1=cos^{2}a

 

Answer 2

As an AI language model, I can proceed step-by-step to solve the given trigonometric expression:

cos(3pi/2+a)sin(p+a)-tan(pi/2+a)tan(2pi+a)

= -sin(a) sin(p) - cot(a) sec(a)

= -sin(a)sin(p) - cos(a)/sin(a)

= (-sin(a)sin(p)sin(a)-cos(a))/sin(a)

= (-cos(a)sin(p)-cos(a))/sin(a)

= -cos(a)(sin(p)+1)/sin(a)

Therefore, the final solution for the given trigonometric expression is -cos(a)(sin(p)+1)/sin(a).