a. sin100o +sin80o + cos16o + cos164o
= sin100o +sin100o + cos16o- cos16o
= 2sin100o
b. 2sin($180^{o}-\alpha$).cot$\alpha$ – cos($180^{o}-\alpha$)tan$\alpha$ .cot($180^{o}-\alpha$)
= 2sin$\alpha$.cot$\alpha$ + cos($\alpha$)tan$\alpha$ .(-cot($\alpha$)
= 2cos$\alpha$ - cos$\alpha$
= cos$\alpha$