Bài tập 3 trang 154 SGK Đại số 10

Câu a:

\(\sin (a + b) + \sin \left( {\frac{\pi }{2} - a} \right).\sin ( - b)\)

\( = \sin a.\cos b + \cos a.{\mathop{\rm sinb}\nolimits}  + cosa.(sin - b)\)

\( = \sin a.\cos b + \cos a.sinb - cosa.sinb = sina.cosb\)

Câu b:

\(\cos \left( {\frac{\pi }{2} + a} \right).\cos \left( {\frac{\pi }{4} - a} \right) + \frac{1}{2}{\sin ^2}a\)

\( = \frac{1}{2}.\left[ {\cos \left( {\frac{\pi }{4} + a - \frac{\pi }{4} + a} \right) + \cos \left( {\frac{\pi }{4} + a + \frac{\pi }{4} - a} \right)} \right] + \frac{1}{2}.{\sin ^2}a\)

\( = \frac{1}{2}\cos 2a + \cos \frac{\pi }{2} + \frac{1}{2}.{\sin ^2}a = \frac{1}{2}(1 - 2{\sin ^2}a) + \frac{1}{2}{\sin ^2}a\)

\( = \frac{1}{2} - \frac{1}{2}{\sin ^2}a = \frac{{{{\cos }^2}a}}{2}\)

Câu c:

\(\begin{array}{l}\cos \left( {\frac{\pi }{2} - a} \right).\sin \left( {\frac{\pi }{2} - b} \right) - \sin (a - b)\\ = \sin a.\cos b - (\sin a.\cos b - \cos a.\sin b) = \cos a.\sin b\end{array}\)

-- Mod Toán 10 HỌC247