IB Math Trig+Mathematical Induction

Posted on February 24, 2022 by Sumant Sumant

Find the value of \sin{\frac{\pi}{4}}+\sin{\frac{3\pi}{4}}+\sin{\frac{5\pi}{4}}+\sin{\frac{7\pi}{4}}+\sin{\frac{9\pi}{4}}

Show that \frac{1-\cos 2x}{2 \sin x}=\sin x, x \ne k\pi where k \in \mathbb{Z}

Use the principle of mathematical induction to prove that \sin {x}+\sin {3x}+ \cdots+\sin{(2n-1)x}= \frac{1-\cos{2nx}}{2\sin{x}}, n \in \mathbb{Z},x \ne k\pi where k \in \mathbb{Z}

Hence or otherwise solve the equation \sin{x}+\sin{3x}=\cos{x} in the interval 0 < x <\pi

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