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(Sin70° + Cos40°)/(Cos70°+Sin40°) what is the value ?

(Sin70° + Cos40°)/(Cos70°+Sin40°) what is the value ?

Grade:12th pass

3 Answers

Arun
25750 Points
6 years ago
Dear Tanuja
 
(sin 70 + cos 40) / (cos 70 + sin 40) 
= (sin 70 + sin 50) / (cos 70 + cos 50) 
= (sin(60+10) + sin(60-10)) / (cos(60+10) + cos(60-10)) 
= 2sin60cos10/(2cos60cos10) 
= tan60 
= sqrt 3 
 
Regards
Arun (askIITians forum expert)
Avijey
13 Points
4 years ago
(sin70 + cos40) / (cos70+sin40)
= sin70 + cos(90-50) / cos70 + sin(90-50)
= (sin70 + sin50) / (cos70 + cos 50)
= (2sin60×cos20) / (2cos60×cos20)
= 2sin60 / 2cos60
= sin60/cos60
= tan60
√3
Sayooj
11 Points
2 years ago
Sin 70+cos40/ cos70+sin40
In numerator we can write cos40as cos(90-50)&in denominator we can write sin40 as sin(90-50).
And also{ sin(90-©)=cos©&cos(90-©)=sin©}
So now
It is... Sin70+sin50/cos70+cos50
Since we see 70  &10 we got the equation 2sinacosb=sin(a+b)+sin(a-b)&2cosacosb=cos(a+b)+cos(a-b)
 
Now sin(60+10)+sin(60-10)/cos(60+10)+cos(60-10)
 
So
2sin60cos10/2cos60cos10
2cos10 get cancelled out and remaining is sin60/cos60=tan60=3^1/2

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