Math, asked by arnab2261, 11 months ago

Hint given : Use tan (A + B) = tan (45° - C)

Topic : Trigonometry

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Thank you..

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Answered by dhruvsh

Here the required and expected thing that you should know is the triple angle formula for tan function.

So, this is a very important Formula and i recommend you to learn this

tan (A+B+C) = (tan A + tan B + tan C - tanAtanBtanC)/1-tanAtanB-tanBtanC-tanAtanC
So,
If A+B+C=45°
So,
tan(45°) = 1 = tan A + tanB+ tanC - tan AtanBtanC/1-tanAtanB-tanBtanC-tanAtanC
So,
tanA+tanB+tanC - tanAtanBtanC = 1-tanAtanB-tanBtanC-tanAtanC
So,
tanA+tanB+tanC + tantanB + tanBtanC + tanAtanC = 1+tanAtanBtanC

Now,
remember,
sigma tanA = tan A + tan B + tanC

which actually sigma in simple terms means the sum of all the like terms occurring in the equation.

So,
we've got
Sigma tan A + sigma tan A tanB = 1 + tan A tan B tan C
Now,
Product of all like terms is represented by π

So,
atlast
sigma tan A + sigma tanAtanB = 1+π tanA

So, the correct answer will be (c)

Hope this helps you !

arnab2261: Thanks, bhaiya.. ☺️

dhruvsh: Ur welcome ｡◕‿◕｡

Soumok: osm!!

dhruvsh: ｡◕‿◕｡

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Hint given : Use tan (A + B) = tan (45° - C) Topic : Trigonometry No spams please.. Thank you.. ​

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Hint given : Use tan (A + B) = tan (45° - C)

Topic : Trigonometry

No spams please..

Thank you..