Question

please solve whole question and step by step explanation ​

Answer 1

Step-by-step explanation:

Given :-

(Sin θ- 2 Sin³ θ)/(2 Cos³ θ- Cos θ)

To find :-

Prove that:

(Sin θ- 2 Sin³ θ)/(2 Cos³ θ- Cos θ)=Tan θ

Solution :-

On taking LHS :

=>(Sin θ- 2 Sin³ θ)/(2 Cos³ θ- Cos θ)

=>(Sin θ )( 1 - 2Sin² θ)/(Cos θ)(2 Cos² θ - 1)

=>(Sin θ/Cos θ) [(1-2 Sin² θ)/(2 Cos² θ -1)]

=> (Tan θ)[(1-2 Sin² θ)/(2 Cos² θ -1)]

We know that

Sin² A + Cos² A = 1

=> (Tanθ)[(Sin²θ+Cos²θ-2Sin²θ) ] /

[(2 Cos² θ -( Sin²θ+Cos²θ)]

=> (Tanθ)[(Cos²θ-Sin²θ)/(Cos²θ-Sin²θ)]

=>(Tanθ)(1)

=> Tanθ

=> RHS

=> LHS = RHS

Hence, Proved.

Answer:-

(Sin θ- 2 Sin³ θ)/(2 Cos³ θ- Cos θ)=Tan θ

Used formulae:-

• Sin A/ Cos A = Tan A

• Sin² A + Cos² A = 1