Question

tan27° tan 32°+tan 32°tan 31°+tan31° tan27°​

Answer 1

Answer:

this is the answer of above question

Answer 2

The value of tan27° tan 32°+tan 32°tan 31°+tan31° tan27° is 1

Given,

tan27° tan 32°+tan 32°tan 31°+tan31° tan27°

To Find,

We have to find the Value of tan27° tan 32°+tan 32°tan 31°+tan31° tan27°

Solution,

From given, we have, 27+32+31=90

So, we consider this form,

S=tanAtanB+tanBtanC+tanCtanA.......(1)

⇒S=tanAtanB+tanC(tanA+tanB)

where A+B+C=90, and C=90−(A+B)

and, tanC=tan(90−A−B)=cot(A+B)= 1/tan (A+B)

or, tanC= 1−tanAtanB/ tanA+ tanB

or, tanC(tanA+tanB)=1−tanAtanB..........(2)

Now, from (1) and (2)

S=tanAtanB+tanC(tanA+tanB)

=tanAtanB+(1−tanAtanB)

=1

Hence, the value of tan27° tan 32°+tan 32°tan 31°+tan31° tan27° is 1

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