Question

5. Find the angle



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Answer 1

Answer:

If 2x and 2y are complementary

And tan ( x + 2y ) = 2

To find :-

The value of cot ( x - y ) .

Solution :-

We are given that 2x and 2y are complementary angle .

Sum of complementary angles is equal to 90° .

↭ 2x + 2y = 90 °

From here we'll get the value of 2y .

↭ 2y = 90 - 2x.

Now x + y =

↭ x + y = 45°

From here we'll find out the value of x .

↭ x = 45 - y .

Now we are given that tan( x + 2y ) = 2 . So ,

Putting the value of 2y here ie 2y = 90-2x

↭ tan ( x + 2y ) = 2

↭ tan ( x + 90 - 2x ) = 2

↭ tan ( 90 - x) = 2

As we know that tan(90-A) = Cot A .

↭ Cot X = 2

We got the value of cot X ie 2

Now putting the value of x in the given equation .

↭ tan ( x + 2y ) = 2

↭ tan ( 45 - y + 2y ) = 2

↭ tan ( 45 + y ) = 2

Now using tan ( 45 + A ) expansion .

We know that tan (45 + y) =

As we know that tan 45° = 1 .So

=

Now applying componendo and dividendo

1 + tan y + 1 - tan y / 1 + tan y - 1 + tan y = 2 +1/2-1

2 / 2 tan y = 3 / 1

1 / tan y = 3

So cot y = 3 .

We got the value of cot y also .

Now expanding cot ( x - y ) by sum and difference of angles .

Now putting the value of cot X and cot y over here.

↭ ( 2 × 3 ) + 1 / 3-2

↭ 6 + 1 / 1

↭ 7

Cot ( x - y ) = 7 .

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Explanation: