Question

Any have solution..........................?​

Answer 1

Step-by-step explanation:

To prove ----->

tan² ( tan⁻¹ 2 ) + tan² ( Cot⁻¹ 3 ) = 37 / 9

Proof ----> We know that,

1) tan ( tan⁻¹ x ) = x

2) Cot⁻¹ x = tan⁻¹ ( 1 / x )

L H S = tan² ( tan⁻¹ 2 ) + tan² ( Cot⁻¹ 3 )

= { tan ( tan⁻¹ 2 ) }² + { tan ( Cot⁻¹ 3 ) }²

Applying first and second formula , we get,

= ( 2 )² + { tan ( tan⁻¹ ( 1/3 ) ) }²

= 4 + ( 1 / 3 )²

= 4 + ( 1 / 9 )

= ( 36 + 1 ) / 9

= 37 / 9 = R H S

Additional information---->

1) Sin⁻¹ x + Cos⁻¹ x = π / 2

2) tan⁻¹ x + Cot⁻¹ x = π / 2

3) Sec⁻¹ x + Cosec⁻¹ x = π / 2

4) tan⁻¹ x + tan⁻¹ y = tan⁻¹ { ( x + y ) / ( 1 - xy ) }

5) tan⁻¹ x - tan⁻¹ y = tan⁻¹ { ( x - y ) / ( 1 + xy ) }

6) 2 tan⁻¹ x = tan⁻¹ { 2x / ( 1 - x² ) }