Double Angle Identites (Trig Ratios)

[Dhkajsd]

Q. from textbook :



Working:



Thanks a lot for any assistance

 

[MarkFL]

Hello, and welcome to FMH!

Your working would be correct if the angle $A$ were a first quadrant angle. But, it's a second quadrant angle. So, what must the sign of the cosine function there be?

 

[pka]

Q. from textbook :

View attachment 12986

Given that $\displaystyle 90o\le A\le 180^o$ means that $\displaystyle 180^o\le 2A \le 360^o$ is in either the third or fourth quadrant.
So then $\displaystyle -1\le\sin(2A)\le 0.$

 

[Dhkajsd]

Than

Hello, and welcome to FMH!

Your working would be correct if the angle $A$ were a first quadrant angle. But, it's a second quadrant angle. So, what must the sign of the cosine function there be?

Thank you, didn’t realise it was so simple it must be negative