Evaluate :
2tan 57°cot 33°2\dfrac{\text{tan 57°}}{\text{cot 33°}}2cot 33°tan 57° - cot 70°tan 20°\dfrac{\text{cot 70°}}{\text{tan 20°}}tan 20°cot 70° - 2cos 45°{\sqrt2} \text{cos 45°}2cos 45°
11 Likes
2tan 57°cot 33°−cot 70°tan 20°−2cos45°=2tan (90° - 33°)cot 33°−cot (90° - 20°)tan 20°−2cos45°=2cot 33°cot 33°−tan 20°tan 20°−212=2cot33°cot33°−tan20°tan20°−212=2−1−1=02\dfrac{\text{tan 57°}}{\text{cot 33°}} - \dfrac{\text{cot 70°}}{\text{tan 20°}} - {\sqrt2} \text{cos45°}\\[1em] = 2\dfrac{\text{tan (90° - 33°)}}{\text{cot 33°}} - \dfrac{\text{cot (90° - 20°)}}{\text{tan 20°}} - {\sqrt2} \text{cos45°}\\[1em] = 2\dfrac{\text{cot 33°}}{\text{cot 33°}} - \dfrac{\text{tan 20°}}{\text{tan 20°}} - {\sqrt2} \dfrac{1}{\sqrt2}\\[1em] = 2\dfrac{\cancel{cot 33°}}{\cancel{cot 33°}} - \dfrac{\cancel{tan 20°}}{\cancel{tan 20°}} - \cancel{\sqrt2} \dfrac{1}{\cancel{\sqrt2}}\\[1em] = 2 - 1 - 1\\[1em] = 02cot 33°tan 57°−tan 20°cot 70°−2cos45°=2cot 33°tan (90° - 33°)−tan 20°cot (90° - 20°)−2cos45°=2cot 33°cot 33°−tan 20°tan 20°−221=2cot33°cot33°−tan20°tan20°−221=2−1−1=0
Hence, 2tan 57°cot 33°−cot 70°tan 20°−2cos45°=02\dfrac{\text{tan 57°}}{\text{cot 33°}} - \dfrac{\text{cot 70°}}{\text{tan 20°}} - {\sqrt2} \text{cos45°} = 02cot 33°tan 57°−tan 20°cot 70°−2cos45°=0.
Answered By
3 Likes
tan (55° - A) - cot (35° + A)
cosec (65° + A) - sec (25° - A)
cot2 41°tan2 49°\dfrac{\text{cot}^2 \text{ 41°}}{\text{tan}^2 \text{ 49°}}tan2 49°cot2 41° - 2 sin2 75° cos2 15°2\dfrac{\text{ sin}^2 \text{ 75°}}{\text{ cos}^2 \text{ 15°}}2 cos2 15° sin2 75°
cos 70°sin 20°\dfrac{\text{cos 70°}}{\text{sin 20°}}sin 20°cos 70° + cos 59°sin 31°\dfrac{\text{cos 59°}}{\text{sin 31°}}sin 31°cos 59° - 8 sin2 30°
