Question
Find the value of the trigonometric expression
\dfrac{\sin8\degree +\cos15\degree\sin7\degree }{\cos8\degree-\sin15\degree\sin7\degree }
Find the value of the trigonometric expression
\dfrac{\sin8\degree +\cos15\degree\sin7\degree }{\cos8\degree-\sin15\degree\sin7\degree }
Using sum identities and half angle identity
\dfrac{\sin8\degree +\cos15\degree\sin7\degree }{\cos8\degree-\sin15\degree\sin7\degree }
=\dfrac{\sin(15\degree-7\degree )+\cos15\degree\sin7\degree }{\cos(15\degree-7\degree )-\sin15\degree\sin7\degree }
= \dfrac{\sin15\degree\cos7\degree }{\cos15\degree\cos7\degree }
=\dfrac{\sin15\degree}{\cos15\degree}
=\tan15\degree =\tan(\dfrac{30\degree }{2} )
=\dfrac{\sin30\degree }{1+\cos30\degree }
=\dfrac{\dfrac{1}{2} }{1+\dfrac{\sqrt{3} }{2} }
=2-\sqrt{3}