Prove that: (i) sinA+sin3AcosA−cos3A=cotA (ii) sin9A−sin7Acos7A−cos9A=cot8A (iii) sinA−sinBcosA−cosB=tanA−B2 (iv) sinA+sinBsinA−sinBtan(A+B2)cotA+B2 (v) cosA+cosBcosB−cosA=cotA+B2cotA−B2
Show that: (sinA−sinB)(cosA+cosB)+(cosA−cosB)(sinA+sinB)=0