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1.sin66°-cos24°=02.cos257°+cos233°=1 |
Answer» EXPLANATION.(1) = sin66° - cos24° = 0. As we KNOW that, we can write cos 24° as, ⇒ cos24° = cos(90° - 66°). ⇒ sin66° - cos(90° - 66°). ⇒ sin66° - sin66° ⇒ 0. HENCE PROVED.(2) = cos²57° + cos²33° = 1. As we know that, we can write cos²33° as, ⇒ cos²33° = cos²(90° - 57°). ⇒ cos²57° + cos²(90° - 57°). ⇒ cos²57° + sin²57°. ⇒ 1. HENCE PROVED.
MORE INFORMATION.Fundamental trigonometric IDENTITIES.(1) = sin²∅ + cos²∅ = 1. (2) = 1 + tan²∅ = sec²∅. (3) = 1 + cot²∅ = cosec²∅. Sign of trigonometric ratios of functions.(1) = in first quadrant all are positive. (2) = in second quadrant only [sin∅ and cosec∅] are positive. (3) = in third quadrant [ tan∅ and cot∅ ] are positive. (4) = in fourth quadrant [ cos∅ and sec∅ ] are positive. |
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