Suppose 9−8cos⁡40∘=a+bsec⁡40∘,where a and b are rational numbers. Then a+b equals.

9−8cos⁡40∘=a+bsec⁡40∘⇒9cos2⁡40∘−8cos3⁡40∘=acos⁡40∘+b----inow,9cos2⁡40∘−8cos3⁡40∘=9cos2⁡40∘−23cos⁡40∘+cos⁡120∘∵cos⁡3θ=−3cos⁡θ+4cos3⁡θ=9cos2⁡40∘−6cos⁡40∘+1=3cos⁡40∘−12∴9cos2⁡40∘−8cos3⁡40∘=3cos⁡40∘−1=acos⁡40∘+b⇒a=3,b=−1∴a+b=2