To expand the expression (1+sina)(tga+ctga)(1-sina), we can first expand the first two terms using the distributive property:
(1+sina)(tga+ctga) = tga + ctga + sin(tga) + ctsina
Next, we can multiply the above result by (1-sina) using the distributive property again:
(tga + ctga + sin(tga) + ctsina)(1-sina) = tga(1-sina) + ctga(1-sina) + sin(tga)(1-sina) + ctsina(1-sina)
Expanding further:
tga - tgasina + ctga - ctgasina + sin(tga) - sin(tga)sina + ctsina - ctsinasina
Finally, simplify the expression:
= tga + ctga + sin(tga) + ctsina - (tga^2)sina - ctga^2sina + sin(tga) - sin(tga)sina
Therefore, the expanded expression is tga + ctga + sin(tga) + ctsina - (tga^2)sina - ctga^2sina + sin(tga) - sin(tga)sina.
To expand the expression (1+sina)(tga+ctga)(1-sina), we can first expand the first two terms using the distributive property:
(1+sina)(tga+ctga) = tga + ctga + sin(tga) + ctsina
Next, we can multiply the above result by (1-sina) using the distributive property again:
(tga + ctga + sin(tga) + ctsina)(1-sina) = tga(1-sina) + ctga(1-sina) + sin(tga)(1-sina) + ctsina(1-sina)
Expanding further:
tga - tgasina + ctga - ctgasina + sin(tga) - sin(tga)sina + ctsina - ctsinasina
Finally, simplify the expression:
tga - tgasina + ctga - ctgasina + sin(tga) - sin(tga)sina + ctsina - ctsinasina
= tga + ctga + sin(tga) + ctsina - (tga^2)sina - ctga^2sina + sin(tga) - sin(tga)sina
Therefore, the expanded expression is tga + ctga + sin(tga) + ctsina - (tga^2)sina - ctga^2sina + sin(tga) - sin(tga)sina.