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tanA=5/6 tanB=1/11 prove that A+B=45° solve the following tan65° cot165°

tanA=5/6 tanB=1/11 prove that A+B=45°
solve the following
tan65° cot165°

Grade:10

1 Answers

Aditya Gupta
2081 Points
3 years ago
tan(a+b)= (tana+tanb)/(1 – tana*tanb)
put values of tanA=5/6 tanB=1/11 to get
tan(a+b)= 1 
tan(a+b)= tan 45
a+b= 45
 
now tan65° cot165°= tan65° cot(180 – 15°)= – tan65° cot15°= – tan65° tan(90 – 15°)
= – tan65° tan75°. Note that it is only possible to calculate values trigonometric ratios for integral multiples of 1½  degree or 3 deg. so it is possible to calculate tan 75, but not tan 65. Hence the 2nd part of question is wrong and can not be calculated (except using a calci, which gives an approx value).

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