Question

Find the value of sin 35° cos 55° + cos 35° sin 55°.

Answer 1

$$\begin{gathered} \sin 35°\cos 55°+\cos 35°\sin 55° \\ =\sin 35°\cos \left(90°-35°\right)+\cos 35°\sin \left(90°-35°\right) \\ =\sin 35°\sin 35°+\cos 35°\cos 35° \\ ={\sin }^{2}35+{\cos }^{2}35 \\ =1 \\ \mathbf{as}\mathbf{,}\mathbf{}\mathbf{sin}\left(\mathbf{90}\mathbf{°}\mathbf{-}\mathbf{\theta }\right)\mathbf{}\mathbf{=}\mathbf{}\mathbf{cos}\mathbf{}\mathbf{\theta }\mathbf{}\mathbf{}\mathbf{;}\mathbf{}\mathbf{cos}\left(\mathbf{90}\mathbf{°}\mathbf{-}\mathbf{\theta }\right)\mathbf{}\mathbf{=}\mathbf{}\mathbf{sin}\mathbf{}\mathbf{\theta }\mathbf{;}\mathbf{}{\mathbf{sin}}^{\mathbf{2}}\mathbf{\theta }\mathbf{}\mathbf{+}\mathbf{}{\mathbf{cos}}^{\mathbf{2}}\mathbf{\theta }\mathbf{}\mathbf{=}\mathbf{}\mathbf{1} \end{gathered}$$