Question

tan 9 tan 27 tan 45 tan 63 tan 81 =1​

Answer 1

Answer:

1

Step-by-step explanation:

To prove---> tan9 tan27 tan63 tan81 = 1

Solution---> We know that ,

tan ( 90 - θ ) = Cotθ

LHS = tan9 tan27 tan63 tan81

= tan( 90 - 81 ) tan ( 90 - 63 ) tan63 tan81

= Cot81 Cot63 tan63 tan81

= ( 1 / tan81 ) ( 1 / tan63 ) tan63 tan81

= 1 = RHS

Additional identities--->

1) Sin( 90 - θ ) = Cosθ

2) Cos ( 90 - θ ) = Sinθ

3) tan ( 90 - θ ) = Cotθ

4) Cot ( 90 - θ ) = tanθ

5) Sec ( 90 - θ ) = Cosecθ

6) Cosec ( 90 - θ ) = Secθ

7) Sin²θ + Cos²θ = 1

8) 1 + tan²θ = Sec²θ

9) 1 + Cot²θ = Cosec²θ