How to Convert Sine and Cosine to Secant for Integration?

[abot]

techniques of inegration, please help

in the attachment there is a problem related to techniques of integration, i fully understand everything until near the end of the problem they answer says

(1/6)o - (1/12)sin2o + C = (1/6)o - (1/6)sino coso + C

and then they convert the sinocoso to sec-1

this part is really confusing...can you help me please...

thank you

 

[VietDao29]

In the attachment there is a problem related to techniques of integration, i fully understand everything until near the end of the problem they answer says
(1/6)o - (1/12)sin2o + C = (1/6)o - (1/6)sino coso + C

?
But... there's no attachment?

 

[HallsofIvy]

Do you know the "double angle formula":
$$sin(2\theta)= 2sin(\theta)cos(\theta)$$

That was what was used.

I'm not clear what you mean by "convert the sin($\theta$)cos($\theta$) to sec^-1"
Of course, sec($\theta$) is defined as $\frac{1}{cos(\theta)}$ so if that "-1" is meant as reciprocal rather than "inverse function", it is true that
$$sin(\theta)cos(\theta)= \frac{sin(\theta)}{sec(\theta)}$$

 

[benorin]

The guy reposted with attachment here https://www.physicsforums.com/showthread.php?t=100046