Question 541148
f tan&#945; =4/3 and cos&#946; = 12/13, where 0<&#946;<&#945;<90°, evaluate without using tables.
a) sin 2&#945;
b) tan 2&#945;
c) cos(&#945;-&#946;)
**
tan &#945;=4/3
sin &#945;=4/5
cos &#945;=3/5
cos &#946;=12/13
sin &#946;=5/13
..
a) sin 2&#945;=2sin &#945; cos &#945;=2*4/5*3/5=24/25
b) tan 2&#945;=(2tan &#945;)/(1-tan^2&#945;)=(8/3)/(1-16/9)=(8/3)/(-7/9)=-72/21
c) cos(&#945;-&#946;)=cos &#945; cos &#946;-sin &#945; sin &#946;=3/5*12/13-4/5*5/13=36/65-20/65=16/65

please check my calculations