Question

sin 9 degree by cos 81 degree + sin 45 degree​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{\dfrac{sin\,9^{\circ}}{cos\,81^{\circ}}+sin\,45^{\circ}}$

$\underline{\textsf{To find:}}$

$\textsf{The value of the given expression}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{\dfrac{sin\,9^{\circ}}{cos\,81^{\circ}}+sin\,45^{\circ}}$

$\textsf{Using}$

$\boxed{\mathsf{sin\,\theta=cos(90^{\circ}-\theta)}}$

$\mathsf{=\dfrac{cos(90^{\circ}-9^{\circ})}{cos\,81^{\circ}}+sin\,45^{\circ}}$

$\mathsf{=\dfrac{cos\,81^{\circ}}{cos\,81^{\circ}}+sin\,45^{\circ}}$

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

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

$\underline{\textsf{Answer:}}$

$\mathsf{\dfrac{sin\,9^{\circ}}{cos\,81^{\circ}}+sin\,45^{\circ}=\dfrac{\sqrt{2}+1}{\sqrt{2}}}$