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Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5959 Points
8 months ago
Dear Student

Given:
sin 67° + cos 75°
In term of sin as cos function and cos as sin function,
it can be written as follows
sin 67° = sin (90° - 23°)
cos 75° = cos (90° - 15°)
= sin (90° - 23°) + cos (90° - 15°)
Now, simplify the above equation
= cos 23° + sin 15°
Therefore,
sin 67° + cos 75° is also expressed as cos 23° + sin 15°

Thanks

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