Question

the value of the expression sin² 63+sin²27 _sin² 90 is
cos² 63+cos² 27

Answer 1

$$\begin{gathered} \frac{{\sin }^{2}63+{\sin }^{2}27}{{\cos }^{2}63+{\cos }^{2}27}-{\sin }^{2}90 \\ =\frac{{\sin }^{2}63+{\sin }^2\left(90-63\right)}{{\cos }^2\left(90-27\right)+{\cos }^{2}27}-{\sin }^{2}90\mathbf{}\left[\mathbf{as}\mathbf{,}\mathbf{}\mathbf{sin}\left(\mathbf{90}\mathbf{-}\mathbf{\theta }\right)\mathbf{}\mathbf{=}\mathbf{}\mathbf{cos}\mathbf{}\mathbf{\theta }\mathbf{;}\mathbf{}\mathbf{cos}\left(\mathbf{90}\mathbf{-}\mathbf{\theta }\right)\mathbf{}\mathbf{=}\mathbf{sin}\mathbf{}\mathbf{\theta }\right] \\ =\frac{{\sin }^{2}63+{\cos }^{2}63}{{\sin }^{2}27+{\cos }^{2}27}-{\sin }^{2}90 \\ =\frac{1}{1}-1\mathbf{}\mathbf{}\left[\mathbf{as}\mathbf{,}\mathbf{}{\mathbf{sin}}^{\mathbf{2}}\mathbf{\theta }\mathbf{+}{\mathbf{cos}}^{\mathbf{2}}\mathbf{\theta }\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\right] \\ =0 \end{gathered}$$