Question Number 10241 by FilupSmith last updated on 31/Jan/17

∫_a ^( a+δ) ((sin(x))/(cos(x+δ)))dx = ???

Commented byprakash jain last updated on 31/Jan/17

((sin(x))/(cos(x+δ)))=((sin(x+δ−δ))/(cos(x+δ)))  =((sin (x+δ)cos δ−cos (x+δ)sin δ)/(cos (x+δ)))  =tan (x+δ)cos δ−sin δ  ∫_a ^(a+δ) (tan (x+δ)cos δ−sin δ)dx  =[−cos δln cos (x+δ)−xsin δ]_a ^(a+δ)   =[−cos δln ((cos (a+δ))/(cos a))−δsin δ]