Question

The value of sin 70 (4cos²20 - 3)​

Answer 1

$\textbf{Given:}$

$\mathsf{sin\,70^\circ(4\,cos^220^\circ-3)}$

$\textbf{To find:}$

$\textsf{The value of}$

$\mathsf{sin\,70^\circ(4\,cos^220^\circ-3)}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{sin\,70^\circ(4\,cos^220^\circ-3)}$

$\mathsf{Using\boxed{\bf\;sin\theta=cos(90^\circ-\theta)}\implies\;sin70^\circ=cos20^\circ}$

$\mathsf{=cos\,20^\circ(4\,cos^220^\circ-3)}$

$\mathsf{=4\,cos^320^\circ-3\,cos\,20^\circ}$

$\textsf{Using the identity,}$

$\boxed{\mathsf{cos3A=4\,cos^3A-3\,cosA}}$

$\mathsf{=cos\,3(20^\circ)}$

$\mathsf{=cos\,60^\circ}$

$\mathsf{=\dfrac{1}{2}}$

$\implies\boxed{\mathsf{sin\,70^\circ(4\,cos^220^\circ-3)=\dfrac{1}{2}}}$

$\textbf{Find more:}$

PROVE THAT:

cos 12 cos 24 cos 36 cos 48 Cos 60 cos 72 cos 84 equal = 1 / 128​

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