Determine the value of \cos 36\degree

Determine the value of \sin 18\degree

Determine the value of \sin 10\degree\cdotp \sin 30\degree\cdotp\sin 50\degree\cdotp\sin 70\degree

Verify the identity \cos 3\alpha =4\cos^3\alpha -3\cos \alpha

Verify the identity \sin 3\alpha =3\sin \alpha -4\sin^3\alpha

Simplify: \sin 50° (1+\sqrt{3}\tan 10° )

If \tan \alpha and \tan \beta are the two real roots of the function

mx^2-2x\sqrt{7m-3}+2m=0 , find the range of \tan (\alpha +\beta)

If \tan \alpha and \tan \beta are the two real roots of the function x^2+px+q=0, find the value of \dfrac{\sin (\alpha +\beta) }{\cos(\alpha -\beta )}

Prove the inequality 1 \leq \sqrt{\sin x}+\sqrt{\cos x} \leq 2^{3/4}

If a\in Z, find the minimum value of the function in terms of a

y = (\sin x+a)(\cos x+a)

Given the function y=\sin x-\cos x+\sin x\cos x, x\in[0,\dfrac{\pi}{2} ], then the maximum value of the function is

Find the range of the function y = \sin x+ \cos x+\sin x\cos x

Find the maximum value of the function y = \dfrac{\sin x\cos x}{1+\sin x+\cos x}

Prove the identity \dfrac{\sin (2α -β) }{\sinα } -2\cos(α -β )=-\sinβ\cscα

Determine the value of \tan20\degree +\tan40\degree+ \sqrt{3}\tan 20\degree\cdotp\tan40\degree