The value of cos²45^o - sin²45^o is_______.

(a)

\(\frac{\sqrt3}{2}\)

(b)

\(\frac{1}{2}\)

(c)

0

(d)

\(\frac{1}{\sqrt{2}}\)

The value 4cos³40^o - 3cos40^o is ________.

(a)

\(\frac{\sqrt3}{2}\)

(b)

\(\frac{-1}{2}\)

(c)

\(\frac{1}{2}\)

(d)

\(\frac{1}{\sqrt2}\)

If \(\sin A=\frac{1}{2}\) then \(4\cos^3A-3\cos A\) is ________.

(a)

1

(b)

0

(c)

\(\frac{\sqrt3}{2}\)

(d)

\(\frac{1}{\sqrt{2}}\)

The value of \(cosec^{-1}\left(\frac{2}{\sqrt{3}}\right)\) is ________.

(a)

\(\frac{\pi}{4}\)

(b)

\(\frac{\pi}{2}\)

(c)

\(\frac{\pi}{3}\)

(d)

\(\frac{\pi}{6}\)

If \(\alpha\) and \(\beta\) be between 0 and \(\frac{\pi}{2}\) and if \(\cos(\alpha+\beta)=\frac{12}{13}\) and \(\sin(\alpha-\beta)=\frac{3}{5}\) then \(\sin2\alpha\) is  _____.

(a)

\(\frac{16}{15}\)

(b)

0

(c)

\(\frac{56}{65}\)

(d)

\(\frac{64}{65}\)