Express $sin\ 67^o + cos\ 75^o$ in terms of trigonometric ratios of angles between $0^o$ and $45^o$.

Given:

\( \sin 67^{\circ}+\cos 75^{\circ} \)

To do:

We have to express \( \sin 67^{\circ}+\cos 75^{\circ} \) 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,

$\sin 67^{\circ}+\cos 75^{\circ}=\sin (90^{\circ}-23^{\circ})+\cos  (90^{\circ}-15^{\circ})$

$=\cos 23^{\circ}+\sin 15^{\circ}$

Therefore, $\sin 67^{\circ}+\cos 75^{\circ}=\cos 23^{\circ}+\sin 15^{\circ}$.   

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Updated on: 10-Oct-2022

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