Evaluate :
sin 80°cos 10°\dfrac{\text{sin 80°}}{\text{cos 10°}}cos 10°sin 80° + sin 59° sec 31°
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sin 80°cos 10°+sin 59° sec 31°=sin (90° - 10°)cos 10°+sin (90° - 31°) sec 31°=cos 10°cos 10°+cos 31° sec 31°=cos10°cos10°+cos 31°1cos 31°=1+cos31°1cos31°=1+1=2\dfrac{\text{sin 80°}}{\text{cos 10°}} + \text{sin 59° sec 31°}\\[1em] = \dfrac{\text{sin (90° - 10°)}}{\text{cos 10°}} + \text{sin (90° - 31°) sec 31°}\\[1em] = \dfrac{\text{cos 10°}}{\text{cos 10°}} + \text{cos 31° sec 31°}\\[1em] = \dfrac{\cancel{cos 10°}}{\cancel{cos 10°}} + \text{cos 31°}\dfrac{1}{\text{cos 31°}}\\[1em] = 1 + \cancel{cos 31°}\dfrac{1}{\cancel{cos 31°}}\\[1em] = 1 + 1\\[1em] = 2cos 10°sin 80°+sin 59° sec 31°=cos 10°sin (90° - 10°)+sin (90° - 31°) sec 31°=cos 10°cos 10°+cos 31° sec 31°=cos10°cos10°+cos 31°cos 31°1=1+cos31°cos31°1=1+1=2
Hence, sin 80°cos 10°+sin 59° sec 31°=2\dfrac{\text{sin 80°}}{\text{cos 10°}} + \text{sin 59° sec 31°} = 2cos 10°sin 80°+sin 59° sec 31°=2.
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3 sin 72° cos 18°\text{3}\dfrac{\text{ sin 72°}}{\text{ cos 18°}}3 cos 18° sin 72° - sec 32°cosec 58°\dfrac{\text{sec 32°}}{\text{cosec 58°}}cosec 58°sec 32°
3 cos 80° cosec 10° + 2 sin 59° sec 31°
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