Express each one of the following in terms of trigonometric ratios of angles lying between $ 0^{\circ} $ and $ 45^{\circ} $$ \sin 59^{\circ}+\cos 56^{\circ} $

Given:

\( \sin 59^{\circ}+\cos 56^{\circ} \)

To do:

We have to express \( \sin 59^{\circ}+\cos 56^{\circ} \) in terms of trigonometric ratios of angles lying between \( 0^{\circ} \) and \( 45^{\circ} \).

Solution:  

We know that,

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

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

Therefore,

$\sin 59^{\circ}+\cos 56^{\circ}=\sin (90^{\circ}-31^{\circ})+\cos  (90^{\circ}-34^{\circ})$

$=\cos 31^{\circ}+\sin 34^{\circ}$

Therefore, $\sin 59^{\circ}+\cos 56^{\circ}=\cos 31^{\circ}+\sin 34^{\circ}$.   

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Updated on: 10-Oct-2022

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