Find the value of :
tan 45°cosec 30°+sec 60°cot 45°−5 sin 90°2 cos 0°\dfrac{\text{tan 45°}}{\text{cosec 30°}} + \dfrac{\text{sec 60°}}{\text{cot 45°}} - \dfrac{\text{5 sin 90°}}{\text{2 cos 0°}}cosec 30°tan 45°+cot 45°sec 60°−2 cos 0°5 sin 90°
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=12+21−5×12×1=12+2×21×2−52=12+42−52=1+4−52=0= \dfrac{1}{2} + \dfrac{2}{1} - \dfrac{5 \times 1}{2 \times 1}\\[1em] = \dfrac{1}{2} + \dfrac{2 \times 2}{1 \times 2} - \dfrac{5}{2}\\[1em] = \dfrac{1}{2} + \dfrac{4}{2} - \dfrac{5}{2}\\[1em] = \dfrac{1 + 4 - 5}{2}\\[1em] = 0=21+12−2×15×1=21+1×22×2−25=21+24−25=21+4−5=0
Hence, tan 45°cosec 30°+sec 60°cot 45°−5 sin 90°2 cos 0°=0\dfrac{\text{tan 45°}}{\text{cosec 30°}} + \dfrac{\text{sec 60°}}{\text{cot 45°}} - \dfrac{\text{5 sin 90°}}{\text{2 cos 0°}} = 0cosec 30°tan 45°+cot 45°sec 60°−2 cos 0°5 sin 90°=0
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Find the value of:
cos2 60° + sec2 30° + tan2 45°
tan2 30° + tan2 45° + tan2 60°
3 sin2 30° + 2 tan2 60° - 5 cos2 45°
Prove that :
sin 60° cos 30° + cos 60°. sin 30° = 1
