value of 3+cot80° cot20°/ cot80°+cot20° is equal to
Answers
Given :
- 3+cot80° cot20°/ cot80°+cot20°
To find :
- it's value
Solution :
= 3 + cot80° cot20°/cot80° + cot20°
= 3sin80° sin20° - cos80° cos20°/sin80° cos20° + cos20° sin80°
= 2 sin80° sin20° + cos80° cos20° + sin80° sin20°/sin100°
= (cos60° - cos100°) + cos60°/sin100°
= 1 - cos100°/sin100°
= tan50°
therefore ,
= ø = 5π/18
Addition information :
- tanø = sinø/cosø
- secø = 1/cosø
- cotø = 1/tanø = sinø/cosø
- 1 - tan(ø/2)/1 - tan(ø/2) = ±√1 - sinø/1 + sinø
- tan ø/2 = ±√1 - cosø/1 + cosø
- sinø = Cos(90° - ø)
- cosø= sin(90° - ø)
- tanø = cot(90° - ø)
- cotø = tan(90° - ø)
- secø = cosec(90° - ø)
ANSWER:-
k=cot80+cot203+cot80cot20=cot(90−10)+cot(90−70)3+cot(90−10)cot(90−70)
⇒k=tan10+tan703+tan10tan70
⇒k=sin10cos70+cos10sin703cos10cos70+sin70sin10
⇒k=sin(10+70)3(2cos(10+70)+cos(10−70))+(2cos(10−70)−cos(10+70))
⇒k=sin802cos60+cos80=sin801+cos80
⇒k=2sin40cos402cos240=cot40=tan50o
Ans: B
\\ ?}^{2ANSWER
k=cot80+cot203+cot80cot20=cot(90−10)+cot(90−70)3+cot(90−10)cot(90−70)
⇒k=tan10+tan703+tan10tan70
⇒k=sin10cos70+cos10sin703cos10cos70+sin70sin10
⇒k=sin(10+70)3(2cos(10+70)+cos(10−70))+(2cos(10−70)−cos(10+70))
⇒k=sin802cos60+cos80=sin801+cos80
⇒k=2sin40cos402cos240=cot40=tan50o
Ans: B
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