Question

Sin square 75 -cos square 75

Answer 1

$\textbf{Given:}$

$\mathsf{sin^275^\circ-cos^275^\circ}$

$\textbf{To find:}$

$\textsf{The value of}$

$\mathsf{sin^275^\circ-cos^275^\circ}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{sin^275^\circ-cos^275^\circ}$

$\mathsf{=-(cos^275^\circ-sin^275^\circ)}$

$\mathsf{Using}\;\boxed{\mathsf{cos\,2A=cos^2A-sin^2A}}$

$\mathsf{=-cos\,2(75^\circ)}$

$\mathsf{=-cos\,150^\circ}$

$\mathsf{=-cos(90^\circ+60^\circ)}$

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

$\mathsf{=\dfrac{\sqrt{3}}{2}}$

$\implies\boxed{\mathsf{sin^275^\circ-cos^275^\circ=\dfrac{\sqrt{3}}{2}}}$

$\textbf{Find more:}$

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